In a desert, water is the scarce currency, so evaporative cooling is expensive. The black-tailed jackrabbit's ears offer an alternative. They are large, thin and richly vascularised, and the animal controls blood flow through them: vessels dilate when heat must be shed and constrict when it must be conserved.
The physics favours shade. Radiative loss works when the ear faces something cooler than itself, so a jackrabbit resting in the shade of a shrub can radiate to the clear sky, which is effectively very cold, rather than to sunlit ground. Classic desert physiology work found that a resting jackrabbit in shade can lose a large fraction of its metabolic heat this way without evaporating water.
The naming trips people up. A jackrabbit is a hare, not a rabbit. Its young are precocial, born fully furred with eyes open in a surface form, whereas true rabbits bear naked, blind young in a lined burrow nest.