Should I cover or not

You will want a piece over the top of the tank to keep moisture from getting to the light and anything else in the hood. Yes the temp will go up a little and your evaporation will be less, or atleast it was in my tank. I would lose a lot of water before and now it is much less and the temp is more constant.

The main concern is the danger of electric shock. It is not wise to use fluorescent fixtures above open water. You could either enclose the fixture itself or cover the aquarium although I think the former would be easier and cheaper. Since it's a custom-made piece, you know better than me which one is more suitable. But just to emphasize, I would certainly isolate the fixture and water somehow.

I built a custom top to hold my florecent lights and I had the same concern as you about the heat building up. I left the back of the top open for better ventilation and I am planning to get mesh to go over it to stop any fish from jumping out. However, I have a canister filter so I have no splashing in my tank and my lights are high enough up that they do not get water near them during water changes or when I am working on my plants. Evaporation is much greater without a top on so this is something I would take into account.

You may also consider including an exhaust/cooling fan(s) in you design. I have them in my lights and they do a great job at reducing the radiant heat.