Refrigeration increases the amount of dissolved O2 in water. Unless other more damaging reactions are retarded by temperature then storage at ambient is probably better.
Again more Internet theories --- have you studied this in a controlled test?
I have and I can tell you that you are "probably" wrong.
Refrigerated sample -- a little bit of XTOL in the bottom of a bottle full of air -- was the best sample, producing around the same density (or a little better) than the second best sample -- a completely squeezed bottle with practically no air, stored at room temp.
I think this is because there is a certain amount of dissolved O2 in the solution and it keeps constant after the bottle is closed. This is especially true when the air is squeezed out, but even with a half-full bottle your theory didn't seem to have a visible effect.
Then, reducing the temperature simply slows down the oxidation reaction as well as other reactions.
As stated before, the samples stored with butane were inferior; especially the one that had only short "puff" of the gas that was quite close to the one with no protective gas stored similarly at room temperature.
Of course, I won't suggest refrigerating everything blindly. I'm just telling the results of my test. If you go too low in temperature, there may be precipitation problems. The best bet would probably be to store in a "cool" place, near the minimum temperature limit by the manufacturer -- usually 10 deg. C.
However, as said before, RA-4 developer is VERY robust and you don't need any special protection for short term storage like a few months. If you are going to keep it for more, then just use
squeezable PET soda bottles and squeeze most of the air out.
In fact, I have had it keep more than a year in a 80-90% full, not perfectly squeezed 1 liter HDPE bottle. So it is not so critical.
And last but not least, as others have already said, DO NOT EVER BUY "ACCORDION BOTTLES"!!! They are the best way to get any photo chemistry go bad. They fail in every aspect they are designed for. On the other hand, I have had RA-4 developer survive even the accordion bottle test, so don't worry about RA-4.