Do you really need an entire room to store supplements?. If you do, you might have a problem. Time for ,
Yes comparing to average Joe I am supplements junkie.
My supplements supply however are contained in about 2'x2'x2' space. Sorry if I made you believe that I am using whole Family room for this purpose.
I wish I could use one whole room in the house just for myself.
Back to original question.
Will the supplements spoil if exposed to (+105F to -15F) range of temperatures.
I don't know if they will spoil or not. Usually they will last well past the expiration date, but they should be kept in a dark cool place.
Cold is usually not a big deal, but anything above 80 or so for extended periods would be a bad idea. Also, and maybe more important, would be the possibility of higher humidity in a garage. That would be a huge problem.
All supplements are in jars with screw tops.
I would open the jars indors where I keep about 75F.
Note on temperature;
for long time my comfortable indoor summer/winter temperature was 77F.
Whenewer I can I am in shorts and no shirt.
Lately I prefer 75F when sitting iddle.
I think it may have to do with my (hopefully) better adjusted thyroid.
Even with "tight" closures somehow humidity always works it's evil if the levels are higher than are normally found indoors. Unless they are packaged under nitrogen or sealed in airtight (vacuum-packed) plastic I wouldn't trust them in a garage.