Where does all the energy in black holes go? The temperature inside of a black hole is almost absolute zero, so particles inside a black hole have almost zero motion.
So if they don't give out any heat or light, where does all the energy it holds go?
Edit:  From an external reference frame, motion inside a black hole all but stops.  (Carlo Rovelli suggests that it takes 14 billion years of Earth time for light to cross the width of a proton.) So does this mean that from our reference the temperature inside the black hole drops to near zero?  And if so, where does this energy go?  In the black hole's proper time (inside the black hole), motion continues as normal, so would the temperature be much greater from that reference?
 A: Energy inside black holes doesn't "go" anywhere. Energy and mass are the same thing ($E=mc^2$). There's a "no hair" theorem that says that black holes can be completely described by their mass (total energy), charge, and angular momentum. So it doesn't matter what the original temperature was of the matter that collapsed to make the black hole -- all that we can observe is the final total energy, some of which may have originally been in the form of heat and some of which may have been mass.
A: The short answer is: To the future!
EDIT: reading OP's question again, they seem to point out, that the temperature of inbound particles is measured by a distant observer as being near zero. But since temperature can be understood as kinetic energy (think: brownian motion for solids), little to no time passes for infalling particles in their own reference frame, so their temperature (not that of the BH itself) is actually unchanged from its own point of view during its full journey. Taking time dilation effects into account, the question seems quite legitimate and not at all ignorant of the subject matter. If no time passes at the EH, no discontinuity or even change can take place in the thermal properties (including quantized momentum) of inbound matter. This is basically a question of quantum gravity at its core.

Basically, all energy of inbound stuff remains in the BH's vicinity, never reaching the EH (as seen from the outside), we call its sum the "mass" (if we ignore angular momentum for the moment) and basically it stays there until the universe gets much MUCH older and colder. Only when the BH is not feeding on any significant amount of matter OR radiation anymore, all this bound energy gradually comes back out in the form of thermal Hawking radiation (also: gravitational waves but that's a different story).
This can only be seen, once the surrounding space has much less energy content compared to todays warm vacuum (due to the CMB). But after a lot of time (and dark energy doing its thing - cooling down the surrounding vacuum), all this energy will eventually be returned to the universe. Once the thermal output of the BH begins to take over its consumption this will very slowly decrease its energy, mass and thereby its radius, accelerating the process.
Sadly, in our epoch, the influx of CMB photons is much greater than the thermal output of any BH we can reasonably assume exists now. Apart from some (hypothetical) primordial BHs, all of todays BHs should be much larger than the current CMB Wavelengths. So they will keep gaining mass from CMB photons alone for an eternity or two, even if no other particles, let alone Stars or other massive objects fall in during this period.
However eventually, when the universe has expanded enough and all matter in their orbits is consumed, even the most massive BHs will start to lose mass again (slowly shrinking and gaining temperature), resulting in a very slow starting burn that accelerates only very gradually at first. However slowly, it should end in a big blast of high-energy radiation in its final moments, when its size finally gets very small. It then should burst in a very intense flash of very high energy radiation (which is itself capable of spontaneously fluctuating into all sorts of massive particles). Theoretically, nothing forbids even whole apes complete with spacesuits to spontaneously fluctuate into being during such highly energetic event, however improbable that may be :P
Some theories assume that a "naked singularity" remains thereafter, whatever that means...
Btw - from what I understand, BH entropy (and by extension, its temperature) is closely linked to the event horizon area (not the singularity's mass or the EH's enclosed volume) - the temperature therefore seems to not be a property of the singularity at all. Look into AdS/CFT correspondence for more details on this.
Warning: Speculation ahead!
Here is a pet theory of mine, which would at least make for some good SciFi in my opinion: The Energy and information content of incoming matter may actually remain outside the Event horizon, since everything "speeds up" in its reference frame. Until the time the BH evaporates, no significant time has passed for the inbound matter, so it doesn't collide with the singularity. Instead, the Event Horizon recedes from it, until the BH is gone completely. From its PoV, Hawking Radiation may not even be noticable or distinguishable from a CMB-like background noise, since "towards the singularity" is now in every direction (it might get pretty hot at some point though). Other than that, it could basically pass trough the BH a few eons later basically unchanged without ever having reached either the Event Horizon or the Singularity. Tidal forces would still be an issue for any monkey falling in I guess but there's nothing that proves a collision with the singularity must take place before the BHs lifetime is over. Sadly, I cannot underpin it with sufficiently advanced math myself... Any takers?
Also - interestingly, the average wavelength always remains proportional to the diameter of the EH, so a dying BH is basically the most point-like light source there can be (at its current wavelength of Hawking Radiation).
A: Firstly I answer question: "How can a very cool object have a large amount of thermal energy":
By having a large heat capacity, by having a large number of internal states, by for example having a very large number of internal particles, that each have a very small amount of energy, which is the coolness requirement at the particle level.
Secondly I answer question: "How can a very cool black hole have a large amount of thermal energy":
By having a large heat capacity, by having a large number of internal states, by for example having a very large number of quantum-states, that each have a very small amount of energy, which is the coolness requirement at the quantum-state level.
Oh yes, a particle is an exited state of vacuum field. So therefore we can replace "quantum-state" by "particle" so we get:
How can a very cool black hole have a large amount of thermal energy?
By having a large heat capacity, by having a large number of internal states, by for example having a very large number of particles, that each have a very small amount of energy, which is the coolness requirement at the particle level.
Now, if we compare this last answer and the first answer, we notice that they are identical.
