You asked if...
Could it be a clog in the coolant system or time to take off the entire heat exchanger?
Can I ask when was the Heat Exchanger last cleaned out..?
If it wasn't recently, it would be a good idea to strip it down and clean it and check/replace the impeller at the same time..
As indicated by Yngmar, the thermostat is there to maintain a set engine temperature, so even at idle it'll remain @ approx 90-95 Deg as the T/stat partially closes, and it'll progressively open as the throttle is advanced...
This will also apply to compensate for a few blockages in the Tube Stack, or a missing impeller blade, The T/stat will simply open further to increase the flow of coolant to maintain the correct temp but it can only do so up to a point.....
I think if your concerned, have a peek inside the H/exchanger and raw water pump.....