This status is not named in-game, but the status effect is caused by Edgar's Air Anchor. Air Anchor's special effect is that once the enemy is hit, it can take one more turn and then it automatically dies.
If the target also has HP Leak, Poison, Regen, or Sap, that may not happen, as Heat treats these as a turn and kills the victim if any of these statuses triggers the healing or damage. Air Anchor is the only item or ability in the game that can inflict Heat. This status can be prevented by being immune to Death, but the self-destruction will trigger even if the victim gains immunity to Death spontaneously before their next action.
Heat status causes the target to become KO'd if any action is attempted. Quina's Blue Magic Mustard Bomb will cause Heat status. Soulcage, Valia Pira, Drakan, and Maliris will use the Mustard Bomb magic, and Tiamat can use a Jet Fire attack that also causes Heat.
Pyretic is caused by the Heat Wave ability of the Five-headed Dragon in the World of Darkness. Rather than causing instant death, those afflicted take damage each time they perform an action (including movement), and can lead to self KO if players don't wait until effect wears off.
Overheated inflicts damage over time with intense heat. It is distinct from the Burnt status, which can occur from Fire damage and deals continuous Fire damage.