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Is having two thermostats for up/downstairs a thing?
Yes, but overkill for your situation. Increase the temp on the thermostat and use the TRVs to keep the temperature consistent across the house. Fit TRVs if you don't have them already.
The numbers on the thermostat are basically meaningless - you just set it to a point where it will warm the coldest bit of the house and then use TRVs to modulate the temperature everywhere else. Total headfuck but that's central heating in 2020. The future is not here yet because both consumers and fitters are largely demotivated and somewhat clueless.
For the full nuclear option get Tado and its robot rad valves.
I find that when we have the wood burner on downstairs
You monster.
Is having two thermostats for up/downstairs a thing? I find that when we have the wood burner on downstairs gets nice and warm but the heating turns off meaning the kids bed rooms are a bit too cold. Any suggestions?