Lots of good ideas above. I’m going to bet the room is an addition and is very lightly insulated and has pitiful HVAC supply.
Ref @Sam_Stone just above here’s a different possible solution.
I have a single story place, but the bedrooms are on the north shady side and the room with the thermostat is on the south sunny side. Given the heat here in FL, the AC kicks on around 2pm steady trying to keep the sunny thermostat room cool and finally kicks off around 10pm never having stopped. Having meanwhile chilled the bedroom down to a miserable cold temp that’s hard to sleep with.
Moving the thermostat to the bedroom was impractical and would simply have triggered the opposite problem as we spend the workday on the sunny side in a different room from the thermostat and would need the AC to respond to the temp need there lest we roast all day with the sun beating on us.
After some searching I got the 2018 model of this thermostat:
https://www.honeywellhome.com/us/en/products/air/thermostats/wifi-thermostats/visionpro-8000-multistage-thermostat-th8320r1003-u/
The key feature is that you can get a remote temperature sensor like these: https://www.honeywellhome.com/us/en/products/air/thermostat-accessories/2-pack-t10-redlink-room-sensor-c7189r2002-2-u/
I don’t care about remote control from my phone. IMO that’s useless puffery. The remote temp sensor is the key thing. And not something I’ve seen Nest, etc., really have the way I wanted it.
I installed the thermostat on the existing wiring in the existing sunny room. And configured it to ignore the temperature sensor built into it. Instead it only “listens” to the portable remote sensor.
In the morning when we start work we bring the sensor in and set it on the corner of a desk in the office. That room is kept comfortable all day long. When we’re done working for the day, we carry the sensor to the living room. And nearing bedtime we drag it to the bedroom.
The end result is the temp in the house is controlled to satisfy the room we’re mostly in at the time. Unlike some people, our daily schedule has almost zero predictability so the e.g. Nest “smart thermostat learning our habits and desires” would be artificial Epic Fail, not wondrous artificial intelligence. And the heat/cool needs of the two sides of the house are so different that no one location for a temp sensor, or even a set of multiple temp sensors, could make happiness.
For sure the OP would need to solve his insulation, drafts/leaks, & heat supply problem first, but once he has enough heat staying in, a remote sensing thermostat may help put the right amount in the room he cares about now.
In my prior 3-story 2-zone house in snow country I had a similar situation as @Sam_Stone. Blocking stairwells with heavy curtains did wonders to keep the heat/cool segregated on each floor. And was really cheap to install. Maybe not relevant to the OP, but someone may find that useful.
Even then a Home Depot oil-filled heater space heater went a long way to keeping our corner bedroom warm in winter.