I don't think it matters if it's not strictly climate controlled, but you wouldn't want to have too much variance (or *rapid* variance) in temperature. A lot of the flaking you see on older games that used backglasses (as opposed to translites) isn't just from old age, it's from the glass warming up because of the lamps and then cooling quickly.
Honestly, I reckon you'd be fine in that sort of a situation, as long as you don't get a lot of humidity where you live. I also wouldn't get something that you'd want to keep in amazing condition or spend a lot of money on. I guess ideally, you'd probably want to look for a cheap(ish) mid-80s game that's in reasonable nick (DMD likely out of the question, unless you find a bargain). Should set you back around $2k. My High Speed is like that (probably a little better than "reasonable", but far from perfect and it could do with a little work) but you can see things like raised/sunken inserts that are indicative of an environment that's not strictly temperature controlled (although the playfield itself is surprisingly good and the backglass is almost perfect. The machine is from Germany, so I don't know how that factors into it).
I'm actually looking at a second machine now. Or what I'd do if I had the room for it. Also somewhat considering moving into a bigger place (single bedroom unit currently) just so I can have more room. Hoping for a Taxi, but if I find one at the right price I'll buy it regardless and either store it or just find room