Puzzle me this....
Glueball, I dont know if you fly the 737, but if you get a high EGT warning on take off or any other engine exceedance, and the decision is to continue, Boeing suggests not to ease back the thrust on that engine as it will invalidate take off performance. At a minimum safe altitude and airspeed (usually 400AGL min) it is then up to the crew to take action as they deem appropriate e.g. reducing thrust on the affected engine.
Interestingly, an Engine Overheat warning is a recall drill, requiring closing of the affected thrust lever. This is not a procedure one would follow on the take off run. We either take off or reject. Consequently, as it is only a Master Caution alert, above 80 knots I'm continuing the take off.
And finally V1 is the speed that we must have taken the first action to reject the take off. It is also the minimum speed, following a failure of the critical engine, at which the pilot can continue and meet the minimum screen height within the take off distance.