No not necessarily - it will keep growing hotter until the black body radiation emitted by the probe matches the power of the radiation hitting the probe. Then it will stay at constant temperature.
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.
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.