Wow.... That seems like a lot of heat from just fluorescents! But yeah, if you are growing coral then a lot of light is probably a necessity. I don't know what is going on there, but whatever is causing the heat rise in the tank, the source is bound to be hot. If the heat "is" coming from the lights (radiation "can" be a significant source of heat transfer, sunlight is about
1 kW / m**2), then there must be something in the tank to absorb the heat (coral?). I wouldn't think that water would absorb much heat, but my heat transfer book says its emissivity is 0.96 where 1.00 is a perfect black body.Eb = Watts / m**2 = emissivity*StefanBoltzmann*(Degrees Kelvin)**4, where StefanBoltzmann = 5.670*10**(-8) Watts / (m**2*K**4)
Black / Gray body radiation heat transfer depends primarily on absolute temperature differences between the bodies and the emissivity of the bodies. The emissivity is spectrally oriented based on the wavelength of the radiation. Since most of the visible light exits the tank, infrared radiation is where the heat is coming from, which is also probably very usefull to the coral.
I would "guess" that the heat is getting in through conduction or convection somehow. I have seen fluorescent ballasts get so hot as to start smoking. Convecting any heat generated by the ballasts away from the tank would be a good thing.
Look for the refrigerator with the best efficiency, or COPR. Then find one that will eliminate heat at some rate above the maximum you think will ever be necessary. If you need 200 watts or 682 BTU / Hour heat eliminated, then anything larger than 682 BTU / Hr will cycle on and off to maintain the temperature of your tank between the high / low temperature set points.
The other thing that might be important is a way to control the flow rate of the tank water through the chiller / refrigerator. Slowing the flow rate down will lower the chiller exit temperature of the water that enters the tank. You don't want your fish to catch a cold when they swim by this flow, so some adjustment in this area may be required. Or maybe you can dump the cold water into the filter pump where it will be well mixed with warm water before coming back into the tank.
Chris. T.