Heat Contract (熱契約; netsu-keiyaku) is a family introduced in BS66, possessed exclusively by the Contract card, Petit Glow, and the Scarlet Flame family cards with Contract Advent that support Petit Glow.
As Petit Glow is The PartnerDragon Glow's form after losing most of his power on Judgment Day, it adopts a new contract name that reads tamer than Flame Contract (炎契約). Unlike the other two released in the same set which takes the second word of the "color families" as their new family names, one possible reason for Petit Glow to use "Heat (熱)" is that "Scarlet Contract (緋契約)" would sound exactly the same as "Mystery Contract (秘契約)" in Japanese, making it confusing.
Cards in the family are either Contract Advent forms of Petit Glow himself, or Spirits that Petit Glow got affiliated with while he was recovering in the forest, or on his journey traveling around Lecoulis following Toa and the others.
