Hot Start? I have never seen a start get to the start temperature limit if all is normal.
If the battery is weak, and the N1 does not reach 12% there is no reason to introduce fuel at all. If you try there will probably be no fuel flow as there is not enough N1 to produce enough fuel pressure to open the minimum pressurizing valve.
Acessory gearbox flooding - too much oil in the acessory gearbox, dragging on the gears there can be a problem. Probably in really cold conditions. That will drag down the N1 and slow the acceleration. I have never seen it but I have heard of it.
A tailwind is not much problem. It usually just causes the exhaust to be injested into the intake and cause the bleed air to stink up the cabin. Bleed air should be off during start anyway. No use taking air away from the engine during start. The cabin sure does not need it then.
If the start hangs at about 30% N1 that usually means the secondary fuel nozzels did not receive any fuel due to a stuck transfer valve. The primaries usually do not supply enough fuel to get that hot by themselves. That increase in acceleration that happens at about 35% is the secondaries opening up.
A milking start - Turning the fuel on and off to control temperature is a NO NO! If the engine and battery are in good shape, I have never seen a start go very much past the normal running temperature limit during start. And that is only on a hot day with a tailwind! 99% of starts don't exceed the normal running red line, and the temperature is moving upward very slowly and about to peak if it does exceed the normal red line.
If you have a weak battery, a tailwind, bleed valves open, you introduce fuel at exactly 12%, and you have any engine problems like stuck bleed valve, bad guide vanes, or other engine damage, then the start could get close to the start limit.
In closing.... If during start the ITT is passing the normal running red line and is not slowing down - ABORT THE START!!!!!! Find out what is wrong.. It should not do that..
I have made thousands of PT6 starts in just about every dash number from -6 to -67 and I have never had a problem... Well there was one problem... A -67A during a windmilling air start that decided to accelerate and then the N1 suddenly dropped to 0%. It seems the N1 Turbine was squeezed by the shroud because the shroud did not heat evenly and distorted!! One hot section inspection, all new blades on the T wheel, and $40,000 later, all was well again. It was not my fault. I did everything correctly.