Something could be rigged for sure with regards to MH lighting, a metal halide pendant light would be great.
However if your just looking at getting say a Bubble tip anemone then PC or VHO should do fine. Softies and some LPS would do well under the same lighting, depending on what you get.
I for one really don't have a heat problem either with my 500watts of MH lighting combined with my 440 watt VHO, it does get warm in the canopy though. I even have fans build into the hood but rarely use them. For some though it is an issue.
Does this 37 gallon cube have its own canopy or not?
Thomas