No, what I am saying you are ignoring basic physics and not even handwaving it. You can not move waste heat from the ship at 290K into a plasma at 200,000K, it is a physical impossibility
Any time you are presented with a non-trivial working system and believe the description you have been given is a physical impossibility, you can usually assume that you have misunderstood part of the explanation. Just bluntly and repeatedly declaring that it is impossible never helps. Instead, point out how you think it works and the contradiction therein, then ask where you have misunderstood. If it truly is impossible, the presenter will have overlooked the contradiction, or something equivalent.
In this case, you are thinking of just transferring heat from a colder object to a hotter object with no other steps involved. That is not what is happening.
Change the plasma's pressure and volume, and you can change its temperature. Drop it to under 290K (or whatever the ship's temperature is), which may turn it from a plasma to a gas. Transfer heat in. If you then return to the former pressure and volume (becoming a plasma once more), the coolant would be at over 200,000K; this may or may not be done before releasing the coolant to space. This is similar in principle to, if much greater in scale than, modern refrigerators - so, literally, saying you can't do this even in principle is saying that refrigerators don't work.
Trouble is the only heat sink you have is the liquid hydrogen that you can't use as a heat sink for long before the hydrogen evaporates, pressure builds up, and your ship explodes.
SOM speaks of using helium (made via fusion from hydrogen), but otherwise this is the method, releasing the helium before it would rupture containment. The helium (hydrogen) does thus effectively evaporate over time: this is represented by the rate of fuel usage by the power plant.
Perhaps you may think this usage rate is impossibly small for the volume of waste heat removed. That, I confess to handwaving as "the magical efficiency of high technology", but we had to take High Guard's numbers as canon and work from there. If that is your quibble, I must defer to authors who went well before we did. I can offer a partial explanation, though: gravitic containment undoubtedly increases the maximum pressure (and thus temperature) that can be contained in a given volume, increasing how efficient this process can be, but there's still a finite limit.