Can My Fish Survive Without A Heater?

How cold is it likely to get overnight?

The good news is that all those species can cope with lower temps. Wrap the tank in anything you have to hand that will insulate it.
When you get the new heater, check the temp before turning it on and bring the temp up slowly. The temp will fall slowly overnight and you don't want to rush heating it back up again.

Leaving the light on will help a bit. It isn't good for fish to have the light on all night but as it's only for 1 night, it'll be OK. Any plants should be OK as well for just the one night.

Fish are a lot more resilient than some people think. I think it's nonsense when people say "My fish needs a temperature of 24 - 26 according to XXXYYY site. Will it survive at 23?" Of course it will, and won't know the difference. Fish today are like today's children, over pampered and over protected, not surprisingly they seem to get more illnesses etc than in the past. I've been reducing my temperatures steadily, everybody still fine at 21 max...........
The article "Whaddya mean it's too hot?" on Seriously Fish should be read by everybody.