The sun would expand, get brighter, and (unless there was some non-magical source of the extra heat) the sun would lose the heat after becoming more active temporarily. It would lose some hydrogen and helium to empty space, as solar flares would increase. The thermal boost would fade into radiation, but not as fast as normal air as the sun is so dense due to gravity that the light actually gets TRAPPED in the middle. (Did you know that sunlight, once generated, bounces randomly from atom to atom within the sun for over 10000 years before it escapes?) The sun would eventually go back to normal, after frying the nearby planets. It will probably regain most of the gases lost through solar flares. Coincidently, I just took a class on this. Sciences involved: Thermodynamics, whatever they call "Study of the Sun", and thermodynamics. EDITS WITH MORE LOGIC: What could cause the sun to heat up? A lot of stuff being thrown into the sun. Gravity would cause the sun to compress even more, amplifying the nuclear fusion process that causes that reactor in the sky to glow. If this were to occur, the sun would grow, but also be more dense than the original sun. Similar to the above story.
If the core temperature of the sun is doubled, that means that new elements have been generated throughout fusion, (larger elements, meaning more energy, and thus more heat). The size of the sun would increase because you have added a new layer of elements for fusion. I don't quite understand by what principle, but I know it has to do with fusion.