If you can find the Model Number for your refrigerator, you may be able to find an illustration of how all the parts fit together that would give you a clue as to what 's wrong.
"Model numbers are usually on the product in a visible location. Look for an aluminum, silver, or white tag that has a number stamped into it. Use that number when searching for parts by model number."
Model numbers on most Sears products, which would include Kenmore appliances, usually have the form as shown by at the above page: (Example:106.48062890).
(My Kenmore top-freezer shows the model number (363.9734716) on a label just inside the door, on the left, inside the refrigerator compartment.)
I don't find a simple path to find an operator's manual for mine, but you might have better luck with a different (more recent) model. Mine is about 9 y.o. The part illustrations, and part listings may not be too helpful unless you have a pretty good idea of what's going on inside your appliance.
Most combination freezer/refrigerators cool the freezer compartment via the compressor and refrigerant cycle, with a thermostat in the freezer. There may be a small "cold plate" in the refrigerator compartment as well, but the refrigerant cycle that cools it is controlled by freezer temperature, so it's more of a "booster" than a primary cooling agent for the 'fridge.
The refrigerator compartment usually is connected to the freezer via an air column, and air convection is supposed to exchange warm air from the refrig side with cold air from the freezer to cool the refrigerator. Typically an adjustable "baffle plate" in the convection air column controls how rapidly freezer air is leaked in/out of the refrigerator section. Except in very expensive (sophisticated?) models, there is no "thermostatic control" of the refrigerator temperature. It's just an open loop compromise between the freezer temp and the outside world.
Since more air convection will occur when there's more heating of the air in the fridge compartment, the open loop is somewhat "self-regulating" if everything works right; but a large change in outside conditions can sometimges require resetting the control.
1. Refrigerator temperature is strongly affected by how often the 'fridge door gets opened, and the "temperature setting" may have to be adjusted if your pattern of access to the refrigerator compartment changes significantly. In a long hot spell, you might just be opening the door a bit more often, which would require opening the baffle (setting a different number on the control) to leak cold air from the freezer at a higher rate.
2. The air passage between freezer and refrigerator compartments must be kept clear. Packing things into either freezer or refrigerator compartments can sometimes block one end or t'other of the air hole. In hot weather, when there is a lot of air exchange, ice can build up, especially at the freezer end. As several have mentioned, fungus and/or furballs could conceivable plug things up.
3. Sometimes, more frequent opening of the freezer door seems to help keep the refrigerator compartment more evenly regulated(?). One theory is that it helps redistribute the ice that otherwise tends to accumulate where the 'fridge air enters the freezer, although I'm not convinced that's the best theory.
Since the freezer is staying cold, it's unlikely that there's a major problem with the compressor/refrigerant machinery, but many "modern" refrigerator/freezer units have one or more "defrost heaters," failure of which can allow ice buildup that blocks the transfer air column. Some units also have internal fans that can "boost" the transfer between freezer and 'fridge compartments, and in some cases the fans may have a thermostat that could fail.
(And even with a floor model on sale, you should have been given the operators' manual and parts list, even if they do seldom put much useful information in them.)
It's possible that the Sears site linked above might also have the JenAire part queried, since they do repair all brands, even if Sears doesn't sell them.