External Double Pole Thermostat to 7500 Watt Forced Air Heater
On the wiring diagram the large and small boxes marked KM are parts of a relay that carry the full current for the coils, any line voltage thermostat will be able to carry the current from the control circuit.
The thermostat can be wired with #14 because the instructionss that are part of the UL listing allow it. I'm guessing there is some internal fuse/fuselink not shown on the diagram.
I am not familiar with full Nest product line, you would need a model with separate control voltage or you would need to build one.