In the sliding of half-spaces with constant friction coefficient, two classes of instabilities are well known: thermoelastic instability (TEI), which occurs for sufficiently long wavelengths and Dynamic Instability (DI), which happens at sufficiently high friction coefficient, and whose growth factor increases linearly with wave number. Although the two phenomena look therefore quite distinct, their coupling is discussed here for an elastic and conducting half-space sliding against a rigid and non-conducting wall. The coupling between thermal and dynamic effects is not always negligible. In fact, surprisingly, new areas of instability are found, called thermoelastic dynamic instabilities (TEDI), similar to TEI at high speeds and DI at low speeds. TEDI lowers the critical speed and friction coefficient in many conditions even to zero. At low speeds, TEDI is ill-posed as DI at small wavelengths, and hence a regularized friction law like the Rice-Ruina one would probably be needed to correct the results.

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