What Galilean said. I think I would model it as a radiation/convection problem to include the lights. You are supplying heat to the tank through the electromagnetic radiation given off by the lights. This will cause the temperature of the water to rise (assuming starting at equilibrium conditions) which will bring about natural convection. If you were to leave the lights on and keep the temp of the room constant, it would eventually reach a new steady state where the heat input to the lights would be balanced by the heat lost to the air. It would be pretty easy to figure out if you knew the required parameters. For the radiation part you would need to know the temp of the bulbs, surface area of the bulbs, and the emissivity. Not all the radiation given off will be absorbed by the tank. Some will go to the tank, some the air, some the light fixture, some the walls in the room, etc. For an ideal, simplifed situation the emissivity is 1 which eliminates it as a factor, but this certainly isnt ideal. Once you know the heat flux applied to your tank, you need to figure out how much heat is lost to the surroundings. To figure this part out you will need to figure out the heat transfer coefficent. For that you will need things like specific heats, thermal conductivities, and viscosity. There are some others but they can pretty much be found from some tables. Also you will need more temperature measurements. However, this will only apply to the water/air interface. The other sides of the tank will have a thermal resistance provided by the glass.
After you have the Q (heat flux) entering and the heat transfer coefficents for the heat leaving through various means you can set them equal to each other. Once the temp of the water goes up enough, the heat leaving the system will match the heat entering. This is kind of like filling a sump. Once it fills to the height of the baffle, the rate at which water leaves is equal to the rate at which the water enters. Anyway, you equate all the Qs and can solve for the temperature of the water. This is also assuming the radiation heat transfer from the tank to the walls is negligable (do you live where it is really cold? are your walls well insulated?).
Also, keep in mind that heat transfer problems are largely solved by experimental data. For a good portion of situations (geometries, flow conditions, etc.) there isnt a theoretical equation that can be solved to get the answer. It's done using correlations based on experimental data for given conditions. There are bunches and bunches of these correlations, some more accurate than others, for each different flow regime. Also, in heat transfer calculations, "good" accuracy is considered within 15-20%. All that hassle for a somewhat close estimate. Like Galilean said, any heat transfer textbook will have all that you need and much more. It really isnt that difficult. There isnt any complicated math involved, and many of the small factors (perhaps radiation heat loss to the walls of the house) can be left out.
All this mumbo jumbo relates to finding out what the water temp of the tank will be, as far as evaporation rate, it would be much more difficult.
Oh gosh, stability, automatic control systems, matlab, laplace, state space...memories.
