A heat beam was any of various forms of focused, infrared energy that could be directed at a specific target. Heat beams may be used to thaw or melt objects; standard hand phasers had a setting for this. More powerful heat beams were sometimes used as weapons, although phasers were generally more effective.
The computer Landru at Beta III had arrays of heat beams that it could use against targets in orbit; these beams were powerful enough to prevent the USS Enterprise from doing much else while under attack, including leaving orbit or transporting to and from the planet's surface. Ultimately, the defense drained enough power that the ship was unable to maintain a stable orbit. Had the situation continued, the ship would have burned up in the atmosphere, probably forcing the crew to flee to the planet's surface. This is likely the sequence of events that led to the destruction of the less-advanced Archon a hundred years earlier. (TOS: "The Return of the Archons")