In general, 4oC is used to prevent protein degradation by proteases. Otherwise, thermodynamic stability of protein can be even higher at 25oC (RT). So, there is no general rule? all depends on the protein of interst - you should be able to use 25oC as long as your protein stable/well folded at that temperature. Of course, you should remember that binding of your protein to a membrane may promote its unfolding/denaturation.
More detailed question is needed for more detailed answer.
possible to bind purified protein on to membrane, it will be efficient, but the protein get denatured and absorb moisture, so don't do with room temperature, use 40C if you need some more efficient means up to 60C you go, more then that means not recommended ., in this no problem you can able to bind with this temperature,
Almost all will get bind in 50C, if you want means try functional group enhancement of protein means 100% effective binding within short time you will get.,
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