Heat is energy. Temperature is an indication of the level of heat in a substance. But the normal way to measure temperature is to observe how the substance interacts with its surroundings - most commonly, by giving off heat to a cooler body, or receiving heat from a warmer one. (A classic thermometer reaches thermal equilibrium with the target, so it depends on such heat transfer.)
Is it possible for a crystal to be so tightly formed that its molecules
have very little heat,
do not receive heat from their surroundings?
Such a crystal would feel warm, despite potentially having a true temperature of a few Kelvin (or less). This substance would then make a superb insulator, just like a true vacuum but without the problem of pressure.
Willing to accept answers that require a small amount of magic, but I want it to be at least plausible. Would be perfectly happy if this is possible and stable without magic, even if it requires magic to create such a crystal.
[EDIT: It appears my use of "temperature" above is strictly incorrect. By "true temperature" I really mean something along the lines of "Joules of heat per kilogram of mass". I'm looking for a way for a substance to have very little heat, yet interact so little with its environment that it is nearly impossible to measure this as a low temperature.]