Can voltage fluctuation cause heater thermostat to flare up?
Yes voltage surges can cause problems with electronic thermostats and other devices.
A whole house surge protector is the best protection for surges on the grid.
I live in Oregon and we have lumber mills in my area (many of them) having customers that were on the same sub station as a mill I had customers that regularly saw what you are seeing and had everything from tv failures to refrigerators failing much more than often.
I installed a surge suppresser in one home similar to the one I had put in my home.
This did not last so we went with a much larger one.
Several years later because the unit had lasted and no more damaged electronics all the neighborhoods had me install suppressors a few did it them selves.
I started recommending the largest whole house surge suppressor that they could afford. One neighborhood every single home installed and almost totally eliminated the problem for years (I moved away but still hear from old customers now and then)
Why get the largest you can afford? If having damage due to surges the devices use MOV’s metal oxide varistors. These dump the excess voltage to ground and if large enough will last for many years but some folks only purchased small-mid sized units and these units degrade when they take a hit larger than there wattage. So the they needed to upsize. If you don’t have a lot of damage a mid sized one may do it.
If voltage spikes are routine and happen daily you may not have a lumber mill but you may have an industrial plant or building with elevators that cause line surges. On the same sub station causing spikes and a surge suppressor at your main panel is the best way to protect your electronics for the entire home from surges.
If you get a surge suppressor make sure it has built in monitoring usually 2 led lights that show the system is functional. (They the suppressors can fail and this means that failure saved equipment in the house).
When installing this kind of equipment I check the torque on all breakers (especially on aluminum wire) do this or ask your electrician to do it only takes a few minutes to verify all the small breakers then adjust the torque for the large breakers and check them (in some cases it can reduce power issues in your home).