Will a double pole, 240V thermostat work here and here? Wiring for 1.5v old brain
You don't have any Neutrals - you appear to be working in North American 120/240 VAC and for a 240V heater setup you have hot, ground, and hot - whites should have been re-marked (red, or black, or any color other than white, grey, or green.) You should do that (I reach for red first in this case, but it's not required to use red, just one of the hot colors.)
You mention 10 gauge wires, and that sets off an alarm bell since typical 240V heater circuits are 20A, and the usual reason you see 10 gauge in that case is that you have (the bad kind of) aluminum wiring. If your thermostats are not specifically rated to connect to aluminum wiring, and the wires are not copper, you may have some additional work to do. OK, you did say this is a 30A circuit, which might make finding suitable thermostats difficult, but should mean the wires are copper.
So, at the junction box where power comes in, in the dining room, you need to join the black wires from the feed and the black wires leading to the living room, and a pigtail to connect to one line side of the dining room 240V two-pole thermostat. If the wires are aluminum, use one side of an alumiconn to connect the two aluminum wires, and the other to connect a copper pigtail. Then you also need to join the whites (remarked red) from the same cables in the same way, and a pigtail to the other line side of the dining room thermostat.  The dining room heater connects to the load side of the dining room thermostat - again, use alumiconns to transition to copper if needed.
All the grounds should be joined, and connected to the box if the box is metal.
That gives you unswitched power to the line side of the thermostat, and unswitched power to the living room thermostat location, so that the heaters work independently.
In the living room, connect the cable from the dining room to the line side of that 240V two-pole thermostat, and the cable to the heater to its load side, again, using alumiconns if you need to transition from aluminum to copper.
In the summer, you might as well shut off the circuit breaker feeding this circuit. That kills the whole thing, while the two-pole thermostats only kill the wires from the thermostats to the heaters.