Thermal transistors that electrically control heat flow have attracted growing attention as thermal management devices and phonon logic circuits. Although several thermal transistors have been demonstrated, the use of liquid electrolytes may limit the application from the viewpoint of reliability or liquid leakage. Here, we demonstrate a solid-state thermal transistor that can electrochemically control the heat flow with an on-to-off ratio of the thermal conductivity (κ) of ~4 without using any liquid. The thermal transistor is a multilayer film composed of an upper electrode, strontium cobaltite (SrCoO_x), solid electrolyte, and bottom electrode. An electrochemical redox treatment at 280 °C in air repeatedly modulates the crystal structure and κ of the SrCoO_x layer. The fully oxidized perovskite-structured SrCoO₃ layer shows a high κ ~3.8 W m⁻¹ K⁻¹, whereas the fully reduced defect perovskite-structured SrCoO₂ layer shows a low κ ~0.95 W m⁻¹ K⁻¹. The present solid-state electrochemical thermal transistor may become next-generation devices toward future thermal management technology.