Breaking of spatial inversion symmetry induces unique phenomena in condensed matter. In particular, by combining this symmetry with magnetic fields or another type of time-reversal symmetry breaking, noncentrosymmetric materials can be made to exhibit nonreciprocal responses, which are responses that differ for rightward and leftward stimuli. However, the effect of spatial inversion symmetry breaking on thermal transport in uniform media remains to be elucidated. Here, we show nonreciprocal thermal transport in the multiferroic helimagnet TbMnO3. The longitudinal thermal conductivity depends on whether the thermal current is parallel or antiparallel to the vector product of the electric polarization and magnetization. This phenomenon is thermal rectification that is controllable with external fields in a uniform crystal. This discovery may pave the way to thermal diodes with controllability and scalability.