I do not used lids, covers or canopies on my tank and I always hang the lights. It gets hot in the summer time where I am and a cover can easily raise the water temp above 85 degrees, even with the AC on.
If you are worried about him jumping out, you can use mesh screen (stretched between a make shift wooden frame) or egg crate to cover. The idea is too let the heat out of the water and allow for good surface O2 exchange. Also, try pointing power heads towards the suface to agitate.
I would definitly get a heater. Stability is important for any animal in a SW fish tank.