The OP has stated the load is a measured, continuous load.
Looking at my post i never asked a my question. If my current continous load is 166amps and i add my 125% = 207.5amps but currently has 200amps OCP. My PAnel is rated for 225A do i need to raise my breaker size to 225AmPS? or can i leave the equipment as is and still be code compliant as far as breaker? The customer wants to add another 20amps circuit to exisint load. whats my max load and I can still be code compliant if all the load on panel is continous load? if not continous load could i have loaded it up to 225a panel rating?
You are already over the breaker's limit for a continuous load. A 200A OCPD is limited to 160A, or 80% its capacity, for loads that meet the definition of continuous. Even tho its a code violation, running it at 166A indefinitely is probably not going to cause any problems.
A 225A breaker is good for 180A of continuous load. If you truly have 166A now, you could add another 20A circuit (eta: to a 225A main) provided its loaded to 14A or less continuous. A 20A circuit can be loaded to 16A continuous.
Aside from changing the breaker size, your feeder may need upsizing too
Imo, your best bet is swapping to a 225A main breaker, pulling this 20A circuit from another panel, or trying to reduce your loads if possible.
Your 120* temp readings are no concern really; pulling a constant 160+A from what is essentially a lighting panel is going to generate some heat