According to what I see the thermostat should begin to open at 194 F, and fully open by 223 F.
I don’t think the temperatures you are measuring indicate a malfunction. Make sure to use the proper coolant spec, replace it periodically, and bleed it of any air pockets, including in the heater core circuit. I presume you’ve already done that. Is the engine cooling fan turning on and spinning like a banshee when the coolant gets hot? If all that’s ok, probably no worries.