moving plants to outdoor building with no heat

i need to move my flowering plants to an out house so to speak, night temp is very low. lights are cfl's. in order to heat inside the grow box can i use a fan heater conected to a termostet inside the grow box, or will this be bad for plants. otherwise night temps might stop or slow flowering any help please

In my experience they work but can dry out the leaves, so turn it to blow AWAY from the plants and keep an eye on humidity.

thanks, so i can leave it in there.cool.thanks stinky