Try turning down your freezer. It is obviously cranked up and the residual cold could be seeping down into the bottom half. Especially if you keep a lot of frozen stuff up in there, your freezer might be working really hard to keep the top half cold and staying on even longer than it usually would if the fridge were running. The insulation between your fridge and freezer probably isn't nearly up to snuff in comparison with the fridge walls.

Short answer: turn your freezer down (or off) and see how it goes.

If you've ever been on a multi-day backpacking trip, you know that bread, hard cheese, non-leafy raw vegetables, fruits, jams and nut butters last perfectly well for two weeks at room temperature.

If you have any of the above that will be consumed within two weeks, and are having their textures ruined by freezing, consider putting them outdoors, or in a cold spot indoors (modern root cellar).

The only things that seem like they would really pose a problem are leafy greens, soft cheeses and milks.

Your fridge doesn't seem to be designed for such frigid (heh, sorry) operating conditions. Its engineers designed it to drop its internal temperature a set amount from the ambient temperature. What they assumed the ambient temperature would be appears to be the issue here - they figured most kitchens or garages rarely drop below 50, so the lowest setting is set to represent, say, a 15 degree change from ambient.
I'd recommend updating your unit to one that's designed to seek an absolute (as opposed to relative) internal temperature target if you don't want to be bothered with moving stuff within the unit or onto the counter.
You can take advantage of the fact that warmer air rises by putting more fragile items on the top shelves of your current unit, and putting hardier stuff on the bottom.
Other than that - water bottles will certainly increase the thermal mass in the unit, and will help prevent fluctuations. They probably won't prevent stuff from getting frozen if the thermostat is dead set on running the compressor, tho. And the cheaper, thinner-walled water bottles companies market as "eco-friendly" these days won't stand being frozen all that well - you might find yourself dealing with leaks when the ice melts.

I agree with Hickepedia. Your fridge was likely designed under the assumption that the indoor air temperature would warmer than the refrigerator temp. The seals might be cracking and the motor might not run properly. Additionally, heat always wants to gravitate to cold, so in this case your room temp might be sucking 'heat' from the fridge. So, really, it seems like if it's getting this cold inside, the refrigerator is useless - unplug it and you'll save electricity.

Also, with keeping a cold house, be careful that nothing else goes haywire such as your plumbing pipes or anything else not designed to operate optimally at such low temperatures.

I have always been baffled by fridge temp settings anyway. Who determines their crazy scales? On one model 5 is the coldest, on another 5 is the warmest. Then they try to help you out with those weird thermometer pictures. The picture above is clear, but my fridge is less clear. Since it's the 21st century, why don't they just include an actual calibrated thermometer so I can set it on like 42 degrees and be done with it?

I'm a bit late to the party, but if it's 40 degrees in your place you're very close to the temperature that a fridge is *supposed* to be at, (in fact, my fridge, which doesn't cool too evenly, seems to hang out around 40, at least where the thermometer is).

Can you simply turn off the fridge portion of the appliance somehow? If some cold is seeping down from the freezer then that should be plenty to keep the fridge compartment cold. Or you could move things to the counter and/or a cupboard with a vent to the outdoors. There isn't much in a fridge that, (IMO), needs to be kept super cold. Maybe meats and some dairy products.

I had this problem with the fridge at my apartment. While I was at an appliance store, I asked a guy about that issue (my carrots and lettuce would freeze too!) He said the way fridge's work is that the freezer mainly keeps the fridge part cool, that's why it would only freeze stuff on the top shelf. Don't know if it's the same problem, but he said it was related just how that type of fridge was made. I guess you could try turning it up and not keeping the freezer as cold.

Was just having similar problems with our vegies and whole bottles of mineral water freezing in the bottom of our fridge!!! Then the freezer/fridge completely went to fridge-heaven one day....the lady that sold us our new (secondhand) fridge gave us some tips, similar to the ones already given above in regards to adjusting temperature settings. She also said to make sure the air vents in your freezer are NEVER covered, so store food towards the center of your freezer. This will ensure the freezer is not overworking. Who knew the science of refrigeration was so complex? Good luck!!