In principle yes, though the situation isn't as clear cut as you describe.

If you could confine a volume of matter within some volume then gradually heat it by adding energy to it then at some point the total energy density would exceed the density required to form a black hole and at that point the matter would start to collapse into a black hole.

However the density of a black hole depends on its size, so the maximum temperature would be dependent on the size of your assemblage of matter.

I suppose you could argue that the smallest volume measurable would be a Planck volume, and you could base your calculation on this. However at such fantastically high energy densities it isn't obvious that temperature has much meaning.

In principle yes, though the situation isn't as clear cut as you describe.

If you could confine a volume of matter within some volume then gradually heat it by adding energy to it then at some point the total energy density would exceed the density required to form a black hole and at that point the matter would start to collapse into a black hole.

However the density of a black hole depends on its size, so the maximum temperature would be dependent on the size of your assemblage of matter.

I suppose you could argue that the smallest volume measurable would be a Planck volume, and you could base your calculation on this. However at such fantastically high energy densities it isn't obvious that temperature has much meaning.