“Right at the limits” is acceptable. If it wasn’t they’d change the limits.
“Takeoff as as soon as the oil temperature is within limits”? Please don’t follow that advice. The manufacturers would say that if it was acceptable. The oil temperature is typically within limits by the time the engine reaches idle. The most it takes is until you do the flight control check. Both are much shorter than the 5 (reduce able to 3) minute limitation.
As tdracer says there’s more to the warm up then just achieving normal oil temperatures.