As Tom said, you'll need (a lot) more batteries to power a 3kW inverter! 3kW at a nominal 12V is a whopping 250A - that's almost at starter motor current levels! The generally-accepted wisdom on the Northern Arizona Wind & Sun solar forum is that drawing more than about 100A from 12V batteries will run you into Mr.Peukert and his limitations on battery currents, unless you have a battery bank a lot larger than your two Group 31s.
To put this into perspective, I have 2kW of solar panels that will charge eight golfcart and/or L16 batteries through two Morningstar TS-MPPT-60 charge controllers. Even with a minimum of 900Ah from eight GC-2s (or more if I use L16s), I don't plan on having a TSW inverter larger than 1500W for general AC loads. I will also use 4/0 cables from each bank of four batteries to their isolator and from the two isolators to the main DC load center - for a 3kW inverter running off 12V I would suggest paired 4/0 cables to minimize voltage loss.
Back to the original question. Assuming your inverter is about 90% efficient, you could be dissipating up to 300W of heat from it at full load! That needs some serious thought about airflow and heatsink orientation. For that much potential heat production I would mount the inverter on perforated 1/4" aluminum sheet - definitely no wood anywhere near it!
John
