  We derive an expression for the magnetic blackbody shift of hyperfine
transitions such as the cesium primary reference transition which defines the
second. The shift is found to be a complicated function of temperature, and has
a T^2 dependence only in the high-temperature limit. We also calculate the
shift of ground-state p_1/2 hyperfine transitions which have been proposed as
new atomic clock transitions. In this case interaction with the p_3/2
fine-structure multiplet may be the dominant effect.
