Can you reach the heat sinks (where temp sensors would be placed) through the case without removing it?
Could you take readings with a laser-thermometer while it's running?
If not, do you have some other temperature sensor that you can secure to the heat sink?
Then, apply some heavy loads, and measured the temperature of the heat sinks with the laser thermometer while it heated up
If that was possible, and you could measure multiple points on the heat sinks, you could find the spot that gets the hottest fastest, then put your own temp sensor there.
Dallas DS18B20 is very popular and suitable for all sorts of controls. There are a million other choices, of course.
The hottest part of the heat sink, getting as hot as it should get when the inverter is under full load, with your fans on, is one set point for that temp sensor. The fans MUST be ON at this temperature. Be sure that you're measuring the hottest temperature that won't cause a FET meltdown like you had last month.
Next, test that spot on the heat sink, with your fans OFF. Obviously you need to turn the power down. Find the steady-state power load that stays below the safe temperature (that you found before) while the fans remain off. Now turn the fans back on, keeping that low power level. This should cool the heat sink down. Once it's cooled down to a steady temperature, this is the LOW set point. The fans must turn ON if the temperature is above this level. They may turn off below this temperature.
Program your Arduino accordingly.
