Here is some useful info from the BX2360 WSM.
Measuring the resistance of the sending unit when your machine seems hot and comparing to the above chart will tell you a lot.
Here is the requested info on the thermostat.
It starts to open around 162 F and should be fully open at 185 F.
IR guns can be useful in terms of diagnosis. i.e. which cylinder is not firing as indicated by a colder exhaust port. However, in terms of producing an accurate "Real World" temp., far less so as Hagrid points out.
If your rad core is clearly clean and is not plugged with debris, I would not worry until the rad cap starts to relieve pressure.
The cooling systems capacity to remove heat increases with increasing temps so you may find at some point it just stabilizes.
Dave