When manufacturers provide tables citing X amount of seconds or X amount of degrees within a particular temperature range, one is playing with fire guessing whether or not the engine has damage. Those tables are really maintenance schedules; they're to determine from a mechanic's point of view, what needs to be done.
Operators may sometimes tell you that the manufacturer allows so long within a maximum temperature range, and that it's okay to go there...five minutes at max temp, for example...what they don't remind you about is that those few minutes could be cumulative over the life of the engine (and even it's subsequent overhauls)...and may have been exhausted long ago.
I once operated an airplane equipped with PT6A-66's, which experienced high temperatures during the start process. My F/O experienced one such event, and I quickly shut it off as the temp climbed rapidly for the limit. Foolishly, I said "here, let me do it," as though my magic touch would make a difference. Not surprisingly, I had to quickly cut it off when the same thing happened again.
The First Officer asked "What shall we do?" I knew exactly what to do. I called the Director of Maintenance. As soon as I told him which tail number I was in, he asked if I was having the temps shoot through the roof on start-up. I said yes, and he said he knew all about it. The airplane had been doing it for three months, he said. I was flabergasted. I asked him what in the name of all things unholy, he thought he was doing continuing to operate that airplane. He told me he had received word from Pratt that so long as the temperature didn't stay there for more than five seconds (well above the start and takeoff limits), he was fine.
I suspected he wasn't telling me everything, having previously been a director of maintenance myself, in an operation flying PT6A's...and I called Pratt directly. The DoM was very wrong; in fact, he was lying to me. I called him back, and he flew into a rage when he learned I'd spoken with the engine manufacturer's technical representatives. He told me I just didn't speak to the right person, and that I should keep asking until I found someone who agreed with him.
Hot starts are very, very serious business. In fact, the most important part of transitioning someone to a turbine engine is teaching them to start the engine. Most operational points after that are a piece of cake. It's the start that does the most damage, most of the time. It's also the one place where a brief moment of inattention can be disasterous, and oh, so costly.