yeah, I'd hate to tell you to stick him under a lamp and then something go wrong. I mean, lots of people DO keep their bettas at room temperature, and their temps drop at night....even though I would never recommend keeping a betta that way long-term. But just for the short-term, you're guy should be ok until you can get a tank that you can heat safely.
(Actually, in all honesty, I keep my betta at room temp, but I'm in the tropics, so room temp means a very
steady 81 degrees
But, if I were a better person, I'd get a heater, just to be safe, to prevent temperature fluctuations. This is also why I never got any goldfish--I really wanted some, but there's just no way I could keep their tanks cool....)