How much heat can roofing underlayment take?

Are you talking on trimming the nail shafts that missed the rafters ? Ring shanks are used for sheeting, and decking , and if you think you could do any better work a layer in between or any contractor can I will gladly provide a 100 point bonus on this site for any one that thinks they can do better!!!

If any nail head below a underlayment would be a problem I would not want anything to do with that material as in the high desert 120 degree temps are normal With +40 to 60 degree surface temps or close to 200f in some areas , yes with degrees colder would still be a problem with your numbers so I question them.

If you are talking about membrane roofing the nails below the surface are not relevant, white membrane reflects heat and is the most common.

Rolled roofing will get really hot but takes a torch to seam the sections still normally below surface temps of black colored roofing.

Possibly more information is needed but after spending decades with the above roof types and others , I have never seen the fasteners, nails or screws cause a problem with heat underneath a roofing material of any kind on the coast or high desert. Well yes even at my uncle Steve’s house in the Mohave desert.

The triflex website you link says:

Do not install under copper, Cor-Ten®, or zinc metal roofing in high altitudes or in the desert southwest. These roofs can reach extremely high temperatures due to the low reflectivity, high absorption, and high conductivity of the metals.

So it looks like the stuff does not like it hot.

Probably you'll have to find a different method,

Experiment with an angle grinder with a 1mm thick cut-off wheel, they have bigger motors than Dremels and thus should cut faster than the Dremel. that should mean that less heat gets into the work.

Experiment with doing partial cuts and then resting to allow the nail to cool.

You might have to resort to hand tools like a single-ended hacksaw.

I usually use an end nipper for roofing nails that miss the rafters ("shiners") because it is fast and easy; bonus for you is no heat involved:

I clipped a bit of the underlayment to experiment with. Cutting a nail with a dremel cutoff wheel on medium speed does produce enough heat to melt the underlayment. Cutting the nail on low speed with breaks, the underlayment seems alright.

This was a conservative experiment. I didn't have a whole nail to play with so I used a clipping. The cut was over the underlayment sample, not 1-1/4in away, but heat spreads quickly through the metal.

I've cut nails with an angle grinder before: the nails get red hot so that's not better. I'm going with end nippers except where I need them really flush in which case I'm using a hacksaw blade.