Karl,
It could be either one, or both. However if your Prosine was showing an over-temp condition, you may want to check to make sure that you have good air flow to the inverter. On some of the Prosine inverters, Beaver installed an air filter over the cooling fan intakes, so if you have one and it is restricted, that may be your problem. Otherwise, just make sure that the inverter has free air flow.
The Prosine has thermostatically controlled fans to keep it cool, so if it has free air flow to cool it , your basement should not be hot enough to cause any inverter problems.
Gerald