Efficient waste heat dissipation has become increasingly challenging as transistor size has decreased to nanometers. As governed by universal Umklapp phonon scattering, the thermal conductivity of semiconductors decreases at higher temperatures and causes heat transfer deterioration under high-power conditions. In this study, we realized simultaneous electrical and thermal rectification (TR) in a monolayer MoSe2-WSe2 lateral heterostructure. The atomically thin MoSe2-WSe2 heterojunction forms an electrical diode with a high ON/OFF ratio up to 104. Meanwhile, a preferred heat dissipation channel was formed from MoSe2 to WSe2 in the ON state of the heterojunction diode at high bias voltage with a TR factor as high as 96%. Higher thermal conductivity was achieved at higher temperatures owing to the TR effect caused by the local temperature gradient. Furthermore, the TR factor could be regulated from maximum to zero by rotating the angle of the monolayer heterojunction interface. This result opens a path for designing novel nanoelectronic devices with enhanced thermal dissipation.