The problem is that any heat a spacecraft produces has nowhere to go. Conduction doesn't work in a vacuum and convection doesn't work without gravity, so the only things naturally cooling a spaceborne object are the solar wind and the object's own thermal radiation. It's quite likely that the Legion is still hot to the touch fifty years after the Lucifer put a hole in it.
(Granted, an thermostat is still needed to keep internal temperatures from swinging between extremes.)
The solar wind is heat source, not a sink. It's the stream of highly energetic charged particles that continually stream off the Sun, and is
much hotter than the outer hull of a ship (like one million K or so). Of course, just because it's hot doesn't mean it actually would cause any measurable heating compared to the Sun's electromagnetic output, since it's extremely diffuse and thus much more of an ionizing radiation danger.
The Legion is also likely very cold, depending on how far away it is from the star it's orbiting (Deneb, was it?). 50 years is more than enough time for all the waste heat from the reactor to be radiated away, and the thermal energy from the beam wouldn't be too much in comparison (yes, I know how much damage it did; quite a lot of that energy went into punching the hole and destroying the ship, not heating it).
You are however correct in that a ship's reactor is going to be simply vomiting up waste heat, and keeping the ship cool when in normal operation (or when it's just in the Sun) is much more of a problem than keeping it warm.
