Not exactly. If, using your Star Trek-style transporter, you instantaneously transported a cubic meter of sun core into empty space, it would radiate a lot of

Not exactly. If, using your Star Trek-style transporter, you instantaneously transported a cubic meter of sun core into empty space, it would radiate a lot of power at first, but by the very fact of radiating all that power, it would quickly cool, especially if you didn't have a good way of keeping it from expanding. But even if you did have some way to contain it, it would still cool pretty fast, since it would no longer be receiving the power input of all the other core stuff around it.