Can somebody help me to figure out what would be the effective test of the cooling system? It started last year when my front grill fans die and I had to replace them with the radiator and all the hoses

LOL. Temperature was ok, however it started going up again, I replaced engine cooling system thermostat, but temperature is still going up on 2000+ RPM.
I know that the radiator is getting hot when temperature is going up so I assumed Thermostat is working properly (radiator temperature in - >105 degrees ; out ~65 degrees).
Front grill fans kick in when engine reaches ~102-105 degrees, I think that indicates that that subsystem is functional too.
I'm thinking about the water pump.... but I have no idea how to test it... if radiator is getting hot pump should be working??? (or how to test it)
I usually see engine working at ~100-~110 degrees (how bad is it?)
If I can keep the RPMs ~ 1500-~1800 RPM I can keep engine in the temperature range above, as soon as I try to slow down after driving on highway engine temp is going up. Looks like keeping engine at 1500 rpms is optimal.
Any ideas welcome.....