Most people think the problem of a cold freezer and warm fridge is with the flow of cold air INTO the fridge, which it can be with a FAN or DAMPER problem; but more often than not, it's a defrost problem:
When a (SxS or top/bottom) refrigerator is working, a small amount of cold air flows from the freezer fan into the fridge and then CIRCULATES BACK from the fridge into the freezer. Air goes from the freezer fan (inside back panel) through a hole/conduit between the freezer and fridge, then through a damper (controlled opening) and into the fridge. Then it circulates back from the fridge through a vent/flap (not close to the fridge air inlet), then through a hold/conduit leading to the evaporator (freezer inside back panel), then over the evaporator coils and into the fan inlet.
No air can flow from the freezer into the fridge unless it has a path to get back to the fan inside the freezer. If the return air flow path is blocked, then the fan simply can't push air into the fridge while the freezer door is closed because if it did, it would create a vacuum in the freezer, which is not possible because of the large vents in the freezer - i.e. the vacuum would then try to suck the air from the fridge back into the freezer. So even though the fan may still be recirculating air hard inside the freezer, it won't blow into the fridge until and unless there's an air path from the fridge back to the fan inlet. If the problem is with a blockage in the air flow path from the fridge into the freezer (as opposed to a problem with the air flow path from the freezer into the fridge), then there will be no air flow while the freezer door is closed. Opening the freezer door suddenly makes air available to the fan inlet from somewhere other than the fridge, which is why air suddenly is able to flow into the fridge.
So the easiest first test of a warm fridge side is to check the air flow into the fridge side with and without the freezer door open. If the air flow into the fridge side is good with the freezer door open and bad without the freezer door open, then the return air flow from the fridge into the freezer MUST be the problem! You now only need to look at the return air path for blockages, because you know that there ARE NO BLOCKAGES (or damper problems) in the air path from the freezer fan into the fridge.
Possible blockages in the return air path from fridge to freezer really only include the return vent/flap which starts inside the fridge plus the path through the evaporator. Clearly my problem is I have a blockage in either the return vent or at the evaporator coils. The return vent's a pretty simple flap that either moves freely or not. It can be propped open if need be to test things. Ice in the return line could be a problem of course. But I see now why warm fridges and cold freezers are most often caused by defrost problems. Air flow 101.
If you have a Freezer on the top model Kenmore, with warm temps in the fridge, AND water dripping onto the top shelf of the lower fresh food compartment (FFC), this is usually caused by a clogged defrost drain. Since Kenmore is not an actual manufacturer of anything, they take other brands, i.e. Kitchenaid, GE, Frigidaire, etc., take their names off and put on a shiny Kenmore nametag. This is a common problem with Kitchenaid refrigerators. You can determine if your Kenmore is made by kitchenaid by looking at the model # tag. the first three digits will indicate the manufacturer, Kitchenaids begin with the sequence, 106.*.If this is indeed how your model # begins, keep reading. Since the water cant go down the drain tubing to the pan at the bottom of the unit, it builds up on the freezer floor, eventually blocking the air return vents from the fridge to the freezer, and the vent from the freezer to the fridge. YOu can check this very easily. Look at the ceiling of your FFC, near the back. toward the sides you will see two square holes, about 2" square, stick your finger and feel around the inside of those holes, do you feel any ice/frost, or do you just feel styrofoam, you might even see frost/ice below the level of your ceiling? This drain usually gets clogged with defrost water that does not completely drain, then of course it freezes, eventually plugging up the drian hole located at the level of your freezer floor, behind the back wall. The water keeps accumulating, and freezing, on the freezer floor, eventually filling in and clogging the air vents..no air flow , the fridge wont cool. The easiest way to resolve this, empty out all contents and store someplace cold for 24 hours...a 2nd fridge, outside in a cooler if its cold like here in chicago. After its empty, unplug, open both doors and blow a fan for 24 hours. Prepare for an abundance of water due to melting ice.
After you defrost, you can plug it back in and it will be fine, HOWEVER, I suggest you take the back freezer wall off, you might have to take a floor cover off first, likely 2-4 screws in both the floor and the back wall. When you have the evaporator exposed, you will see a black cal rod defrost heater underneath the evaporator, as well as your drain hole just to the right of center underneath both heater and evaporator. Take a piece of 12-14 gauge solid, not stranded wire, removing the insulation and exposing the entire 6-8" piece of copper wire. wrap the wire around the diameter of the cal rod heater, 3-4 turns should be sufficient, and stick the other end of the wire down that drain hole. This will melt any ice that will build up in the future, everytime your unit goes into defrost cycle, so this wont happen again.
If air vents are clear of frost/ice, next thing to check is the back wall of your freezer, does there appear to be frost/ice/snow on the back wall? If so, your unit is not defrosting. On most Kenmores, this is usually caused by your defrost timer, located in the canopy mounted at the top of the FFC on Top freezer models, or your defrost thermostat, which is clipped onto the evaporator coil inside your freezer. Again, if its a 106 model Kenmore, this thermostat will have a pink and a brown wire coming into/out of it. My suggestion, if it isnt defrosting, change both. tjhe defrost control will connect with a plug, but you will have to hard wire the thermostat, ( cut wires from old, strip wire, and connect using wire nuts and electrical tape.)
Since y ou mentioned the water accumulation, more water recently, my diagnosis would be the former versus the latter, as the lack of actual defrosting coincides with lack of defrost water, however I'll never say never.
If your unit is a side by side model, check for ice on freezer floor...clogged drain. Check again for frost/ice on back wall, not defrosting, check same two parts, (the heaters rarely go bad on Kitchenaids, but never say never) You should also check for air flow into fridge, even if no frost / ice visible on back wall. Open the FFC door, and locate the air vent near the top, back of the fridge, on the left wall. While depressing the door switch, AND WITH THE FREEZER door closed, put your finger/hand near that vent. Do you feel any cold air? If you dont, you could have a bad door damper, not uncommon, or a bad damper control--> the temperature control WITHOUT the off or "0" position.
If any of this seems a bit overwhelming, I suggest you have a reputable repair technician check your fridge.
Oh, and lastly, you WILL NOT have two compressors, one for each compartment, nor will you have two sets of defrost heating elements, one for each half.
ALL cooling for 99% of refrigerators made in last 25 years takes place in the freezer, with the fridge being an empty box, except for an air intake vent, and an air exhaust vent which leads directly back into the freezer. When a refrigerator unit seems to still be cold in the freezer, but not cold enough or not cold at all in the FFC, its ALWAYS going to be caused by lack of air flow. But as you can see, there are a few things that can cause that lack of air flow.