Strictly this is more of a Mechanical Engineering question. Anything involving heat transfer is more frequented by MEs and ChemEs.
I've done these calculations before but they can get sufficiently involved that I'd probably never do them for free for anyone. You may want to try the ME or ChemE forums - these folks will be better at estimating off these kinds of things off the top of their heads than I or any EE can.
Honestly the easiest and most accurate answers will come from the manufacturer of the inverter and not a hand calculation by someone here. This is the kind of thing they should already have done, at least for still air rather than forced air cooling (the former is a more worst-case situation).
If you go it alone, I'd recommend a copy of the ASHRAE handbook for formulae and an engineering heat transfer textbook for explanations. All this is why I defer to my ME brethren (and sistern/cistern) when I can for heat transfer questions (my own or others').