I use red heat bulbs on my rack and I place the bins 6-8 inches from the light so it doesn't get too hot. I've had those and critter carriers melt because of that. You need a few inches of space so it's not like a heat beam on one spot. If you can't clip or hang the bulb above or beside the tank then you can rest assured they do fine at room temp. However the low 70s will not get you high breeding rates and they will grow slower.
Good luck and let us know what solution you went with.
Ps, if you have forced air heatin like I do, set the bin beside the vent so when the heat kicks on the bin gets warmed up. I keep several bins huddled around a heat vent and this works really well for mine.