Wiring thermostat for 120v heater

The code requires that all ungrounded conductors are disconnected. The double pole thermostat that you have described is for a 220v heater.
2 wire method


It is crucial for your 120v heater, that there is 120v from black to white! Not 220v
L1 and T1 pass through when there is a demand for heat
L2 and T2 pass through when there is a demand for heat

A house wired prior to 2008 would have the white wire , wire-nutted through even if it was 220v heater system; Where a house wired after 2008 the white wire would have landed on the L2 and again on the T2

If the supply voltage is 120v; Then you only need the L1-T1 side of the thermostat and the L2 and T2 wires are not needed

With the current code the 220v system is required to break all of the line wires.
220v systems that used baseboard heaters did not require a neutral wire; Instead the white wire carries 120v to ground and the black wire also carries 120v to ground. Across each other they measure 210-240v
(A 120v heater should not be used in this situation)

L1 being black (powered wire) and L2 being white (powered side)
The black of the (heater wire) T1 and the white of the (heater wire)

This method will work on the 120v heater as well but is not required. On a 120v heater the thermostat only needs L1(black powered wire) and T1 (Black heater wire)

The white wires can be wire-nutted together and stuffed in the back of the box

3 Wire method

If there is a red, black , white, and ground in the box; This would be a three wire system.

The black wire will be 120v to ground, the red will be 120v to ground, and the white will be a return path. From black to red will be 220v

Use the black powered wire as L1 and the black of the heater wire as T1. Tie the white of the powered wire directly to the white of the heater wire,
In this situation the thermostat only separates and connects the power wires together when there is a demand for heat.