Well, you could utilize a simple thermostat for a furnace?

OR, you could utilize a thermostatically controlled tempurature switch utilized in a radiator fan. Racing applications use them all the time. You may want to look at this as your solar panal is already producing DC current. Instead of using an AC fan that you would have to run through your converter box, you could simply utilize a DC fan utilized in radiator applications and draw the current direct from your solar panel. Or prior to it going through your converter/inverter.

Either way, I would say your serch could/should contain thermostatic control switch or thermostatic fan control switch.

Talk to a heating and cooling place. They might just have exactly what you are looking for (AC or DC)