Need help wiring a new double pole line voltage thermostat
OK, quick terminology issue: Single-pole and double-pole.  The poles are channels, which could have any purpose.  A single-pole switches one channel; a double-pole switches two.  (ignore the "st").  (source)



For a thermostat, one pole is sufficient to turn the heaters on and off.  For the other pole, you'd simply bind the wires together - and I think that's what's been done with the white wires. 

You say this powers 2 heaters, and that's the dead giveaway.  The power supply would be one group of wires, and the outputs would be two groups.  Now look at what's going on with that switch: you have one wire spliced into the red thermostat wire (that must be the power supply) and two wires spliced into the black wires (those must be the heaters).  

Follow the one wire and it goes to the Romex on the right.  That Romex goes to the power source, clearly, and its wires should be considered "LINE" (always-on).  Which means the white wire in that bundle is the other pole.  

The other Romex cables go to the heaters, and they are "LOAD" (switched). 

This wire is /2 Romex since there's no red wire. (ground is not counted, so /2 means black and white).  The yellow sheath suggests 12/ since some manufacturers recently adopted that as a color code.  The markings on the sheath say for sure. 

Are the white wires hot (240V) or neutral (120V)?   We can't tell.  It would be wired the same either way.  240V heaters don't need neutral, so they use 12/2 or 10/2 wire, and re-designate and supposedly, re-mark the white as another "hot".  Somebody went to a lot of trouble to put red tape on the Romex cables... shrug.  In the old days, marking wasn't required if the use was obvious.  

So we must go down to the breaker panel.  Looking at the layout, it should be obvious that there's a unit of "space".  If the breaker takes 2 spaces, it is a 240V circuit. There won't be many of those.

Simply, turn off one at a time and see what it knocks out. Generally there is one thing on each 240V circuit (well, oven and stove may share a circuit).  This is a good time to mark those breakers once you figure what they control. Not least it helps you eliminate; heaters are very annoying to test because they take a long time to make noticeable heat. 

If it's a 240V breaker, obviously, these are 240V heaters. 

Although the smart thermostat may not care if it's 120V or 240V.  It needs to power itself, but it may be inherently multi-voltage.  Many things are nowadays. 

It goes without saying that you have to find the breaker in order to change the thermostat.  If you don't realize that, you should not be doing electrical work.