I'm installing 6000 watts of electric baseboard heat in a rental and want to install it all on #10 copper Romex. I want to know if I can install it on a contactor in basement for control of it. I also want to control it on and off with a 120 volt thermostat to coil of contactor.

Sure, your plan is typical of a 30 amp heat circuit, and will work fine. If you have any specific questions, let us know.