We report on changes in the thermal conductivity of solid-state synthesized MnxMGe (M = Co, Ni, 0.98 < x < 1.02) alloys through their temperature-induced martensitic structural transition. The thermal conductivity is measured by time-domain thermoreflectance. Mn1.014NiGe exhibits an increase in thermal conductivity from 11 to 15.5 W m(-1) K-1 from approximately 575 to 625 K, and Mn1.007CoGe exhibits an increase in thermal conductivity from 7 to 8.5 W m(-1) K-1 from 500 to 550 K. In MnxNiGe, the transition temperature and the magnitude of the change in thermal conductivity are strongly dependent on the alloy composition. Our study advances the fundamental understanding of the thermal transport properties in the MnxMGe(M = Co, Ni) family of alloys and opens a new direction in the search for solid-state phase transition materials with potential applications as thermal regulators.