How do I install a high intensity infrared heater and thermostat
Do not hook this to mains power. 

Get yourself a 24VAC, 40VA transformer, which is common as dirt, $12, and widely used on conventional furnaces.  They typically mount either on the cover of a 4x4 square metal junction box, or in a 1/2" trade size knockout on the side of such a box.  Both these wiring methods put the mains power inside the metal junction box, and the 24VAC power on the outside.  


The transformer provides two 24V terminals: R and C.  
Your thermostat requires 3 wires: R, W and C.  
Your heater needs W and C.  


The R wire should be red.  The W wire should be white.  The preferred color for C is blue, but that may not be practical in 2-3 wire cable.  

This setup, which is mandatory for this heater, will allow you to use almost any thermostat on earth including smart 'stats like the Nest. 

If you ever anticipate doing A/C or heat pump you want at least 6 wires in the cable to the thermostat.