Mainly, the very hot thing being described that way is also very small so has little total heat energy. That same amount of energy spread out over a very large mass will only provide a fairly low temperature. That is, heat is not temperature. Temperature is a measure of the total kinetic energy (energy of motion, vibration, spinning, and wiggling of atoms, basically) of the mass under examination. Heat is the sum of all that energy plus the energy hidden in the structure itself (the arrangement of atoms uses energy too and can absorb heat). Same total heat spread over larger mass leads to much lower average temperature.
The amount of energy in a very small object will be rapidly diluted if allowed to leave and spread to another much larger mass. If each atom gives all its energy to 100 other atoms, the other atoms will only have 1/100 of the energy of the original atom (on average). And there are way more than 100 atoms in the surroundings to each atom in the hot item so temperature rapidly decreases from the source. The amount of energy is the same, but it is shared with a hugely larger number of atoms, so the temperature is way lower. This would, of course, quench the very hot item very quickly if new energy is not constantly added.
Somewhat like smashing a cue ball into the racked balls at the break, but way more dilution because there are an absurdly much larger number of atoms in the surroundings than in the tiny but very hot mass.
Making a hot spot does not mean everything around it will rise to the same temperature very quickly though. It takes time and requires that energy is constantly added to the hot thing, or the hot thing will cool off fairly quickly and stop being hot. In your question, you ask why the containers don’t melt. Well, a melting container would suck heat and cool the experiment so the high temperature would be very short lived. So, for such experiments, we don’t use a container that will melt over the course of the experiment. For many purposes, highly heat tolerant and heat resisting substances like ceramics can be used, In many cases, the experiment will involve a tiny mass (like micrograms or milligrams at most) so there is little heating of the container except over time. Often, when heating of the container would be a problem, the material will be suspended in a magnetic field withing a high vacuum, so there is as little interaction with surrounding mass as is possible. Interaction with mass will quench the object, and that is not at all desirable.
Nuclear bomb explosions that are as hot as the sun do involve a considerable amount of mass (generally kilograms of nuclear material, not tonnes) and do release a lot of energy, so the region affected by extreme heat is fairly large (enough to set a city on fire, but most of the city never gets even close to as hot as the sun; 500 degrees is a lot different from 5000 degrees). It is still only in the very heart of the explosion/reaction that the temperature is as hot as the sun. Temperature drops rapidly with distance as the surroundings get heated and the initial energy is spread out over a large volume of mass.
The sun’s heat is only a lot here on earth because the sun is so dang big (it is HUGE) and the energy it loses at surface is continually replaced by new energy from inside.
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