This talk will be about an approach to constraining conformal field theory (CFT) data at nonzero temperature using the conformal bootstrap. We focus on thermal one- and two-point functions of local operators on the plane. By studying the analytic properties of thermal two-point functions, we derive a "thermal inversion formula" whose output is the set of thermal one-point functions for all operators appearing in a given OPE. This involves identifying a kinematic regime which is the analog of the Regge regime for vacuum four-point functions. We test the formula in mean field theory and the critical O(N) model at leading order in 1/N. We explain how the inversion formula and KMS condition may be combined to constrain CFTs at finite temperature.