What type of body fat do bats rely on during hibernation?

Bats rely on brown fat during hibernation. This specialized tissue stores energy and helps a bat rapidly generate heat when it periodically arouses from torpor.

Brown fat differs from ordinary white fat in its cellular structure. Brown-fat cells contain many mitochondria and small lipid droplets; the mitochondria use stored fuel to produce heat rather than simply supplying energy for movement. This process is called non-shivering thermogenesis and is especially useful for a small mammal emerging from a cold hibernation state.

Bats generally accumulate substantial fat reserves before winter, when insects become scarce. During hibernation they lower their metabolism and body temperature, conserving energy between brief arousals. Brown fat is especially important during those arousals, when the bat must warm its body before drinking, changing position, or responding to threats.

White fat is not irrelevant: it provides a major general energy reserve and insulation. But brown fat is the canonical answer because of its specialized heat-producing role. Fur provides insulation rather than metabolic fuel, and blubber is associated mainly with aquatic mammals rather than bats.