Heat is energy that in being utilized by a heat engine is converted into something else. It is already gone. It exited the system as "work" or electricity.
If the heat were still there needing to be removed, that would be a violation of conservation of energy.
Unless you're proposing a new physical force (outside of electromagnetic, weak nuclear, strong nuclear and gravity) then I think your, and Tesla's, reading is a bit off. Same with some Thermodynamic items like Entropy.
In a physics sense there is no "heat", only energy levels. The fact that you can use work to either add or subtract energy from a system is no big deal, but the net energy used as work is always greater than the net energy added/removed from a system (i.e Entropy exists). You can approach, but never exceed unity in your system, Entropy must increase somewhere.
If you find a system where Entropy doesn't exist or is not increasing then you haven't accounted for all the factors.
I have a hard enough time reading Tesla's write-up since it's in this 19th century gobbledy-gook presentation style that I can't be arsed to simplify into known terms that have been discovered and elucidated over the past 150 years. But his idea of Heat flowing to a cold hole perpetually seems from my reading to not include all the pertinent facts about the system he discusses.
You can take the idea of coupling your cold hole to space as a sink, but your energy account will then show an increase in entropy in space. Plus, you have to define HOW this coupling is occurring and what the physical attributes are w.r.t. this coupling (heat flux, etc.).
Certainly not. Tesla writes in broad grandiose abstractions and uses metaphors and illustrations that are difficult to follow. He assumes too much, writing as if everybody knows all about whatever subject he happens to touch upon and all that is implied therein. He trollops through various scientific arenas, gas liquefaction, refrigeration, energy conversion, heat engines, thermodynamics, etc. etc. as if everybody knows what he's talking about.
Just for example, he writes at one point:
"This would be an inanimate engine which, to all evidence, would be cooling a portion of the medium below the temperature of the surrounding, and operating by the heat abstracted." (Here he just described the possibility of a thermopile reaching from the warmth of earth's atmosphere into the cold regions of outer space)
"But was it not possible to realize a similar condition without necessarily going to a height? Conceive, for the sake of illustration, [a cylindrical] enclosure T, as illustrated in diagram b, such that energy could not be transferred across it except through a channel or path O, and that, by some means or other, in this enclosure a medium were maintained which would have little energy, and that on the outer side of the same there would be the ordinary ambient medium with much energy. Under these assumptions the energy would flow through the path O, as indicated by the arrow, and might then be converted on its passage into some other form of energy."Here he is describing a heat engine in about the most simplistic and abstract way possible without specifically naming the type of engine or even the fact that he is talking about a heat engine at all.
"by some means or another" forget about the actual working mechanisms involved.
Tesla was pretty much on top of all the latest scientific advances of his day, and conducting experiments and building new devices that put him years ahead of his time. This was a popular article for a magazine addressed to general audiences. He was not able to use specific technical scientific jargon in that forum.
On the other hand, we could possibly conclude that he said "by some means or another" because he was completely clueless in regard to how such things operated or even what to call them.
Personally I'm inclined to think that the failing is on the part of the reader considering the extent to which the modern world is dependent on his discoveries and inventions.
So, how does a heat engine work?
Why do you need a temperature difference?
How does a heat engine exploit random molecular motion (Heat) and bring order to that motion so as to be able to control it and direct it in such a way that usable energy might be extracted?
What methods have been employed to accomplish this?
What are the component parts of such a device? Could we improve it?
How many different types of heat engines are implied in that "by some means or another"?
How does a heat engine actually convert heat into work? How does a refrigeration system work? How could these two systems possibly be brought together in one mechanism?
It might take years of dedicated study and research to know exactly what is implied in those few flippant words: "by some means or another".
Personally, I for one do not want to underestimate the mans genius. On the other hand, maybe I give him too much credit. Who knows?
But the more I've studied heat engines and thermodynamics and the liquefaction of gases, and refrigeration systems and heat pumps and the like, the more evidence accumulates to suggest that Tesla may have been right after all.
His whole essay was written in direct contradiction of the the conclusions of some of the greatest thinkers of his day, the fathers of thermodynamics.
He wrote: "I read some statements from Carnot and Lord Kelvin (then Sir William Thomson) which meant virtually that it is impossible for an inanimate mechanism or self-acting machine to cool a portion of the medium below the temperature of the surrounding, and operate by the heat abstracted. These statements interested me intensely. "
He then goes on to say in effect: "Hey wait a minute guys, you overlooked something. Yes it could very well be done thus and such"
Then he goes on to say: "This seemed to be contrary to the statements of Carnot and Lord Kelvin before referred to, but I concluded from the theory of the process that such a result could be attained."
He was not unfamiliar with the subject of thermodynamics. If he did not know the subject quite well, he could never have located the chinks in the armor.
OK, so he was a bit of a nut case who fell in love with a pigeon and sometimes believed he was receiving communications from aliens,... just the same I'm a bit reluctant to dismiss what he has to say without some kind of trial.
I'm inclined toward experimentation as a final proving ground and I can't find any record of any experiment based on Tesla's alleged earth shaking "discovery" which if true, pretty much puts the second law of thermodynamics in the toilet and opens the door to a whole new way of harnessing solar energy.