Assuming passive systems? It doesn’t work that way.
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?