2,500º F is merely the temperature the probe is expected to reach at that distance. if it were to stay at that distance indefinitely, it would grow much, much hotter as it absorbed more energy from the sun.
It's a standard undergraduate problem to work out what this equilibrium temperature is for a flat plate at a distance from the sun equal to the Earth's orbital radius.
Interestingly the result is only a few 10's of degrees less than the average temperature of the real Earth - the difference is due to the Greenhouse Effect.
For the probe one could easily do the maths but I could believe that at 4 million miles that equilibrium temperature is 2,500F.
* With "eventually" being "assuming a stable state for infinite years" which is of course not how astrophysics actually works.
You’re talking about heat (think ‘amperage’), where temperature is more like voltage.
You can’t get above a specific temperature merely by transferring more heat, or losing less heat, etc.
Upper bounds of temperature is still going to be limited by the temperature/frequency of the input energy, barring energy loss which can reduce it.
The solar atmosphere layers have specific maximum temperatures that limit the maximum temperature of objects exposed to them or the radiation from them.
but you can keep absorbing radiation indefinitely
so the equilibrium temperature will depend on the incoming radiation and ensuing outgoing radiation as dictated by the material makeup of the thingy
Once the object has reached the temperature of the source of the radiation (assuming radiative heat transfer), it reaches equilibrium and it will radiate away at the same rate it is absorbing (as a black body). Per the 2nd law of thermodynamics.
It’s why there is a maximum temperature with concentrated solar too - regardless of magnification, you can’t exceed the temperature of the surface of the sun the light was emitted from. Attempted to do so will actually heat the sun (or some other thing) through radiative thermal heat transfer the other direction.
It’s also why radiative heat transfer can’t be used to produce infinitely high temperatures by having a large emitter near a tiny absorber (like a speck of dust) in a vacuum.
If there is some kind of heat pump or laser or the like which you a providing power, then that doesn’t apply of course, but for pure black bodies it does.
If you have some way to let an object absorb radiation, while emitting no radiation even when it is as hot as the source of that radiation, then you have something pretty special going on eh?
Part of it is due to the ‘Principle of Etendue’ [https://en.m.wikipedia.org/wiki/Etendue#Conservation]
What confuses people I think (practically) is that the actual high temperature (~4500F) is far beyond the limits of a useful highest temperature in 99% of situations we might want in engineering. A spacecraft hitting that temperature is going to be a molten piece of scrap long before it hits that point.
But the limit does actually exist - it won’t somehow hit 10,000F for instance. That is also why we can’t produce infinitely high temperatures with a huge magnifying glass - the highest we can hit, regardless of how big it is, is still ~ 4500F. Higher temperatures need something like an electric arc furnace, or LASER.