  Direct observation of temperature dependence of individual bands of
semiconductors for a wide temperature region is not straightforward, in
particular. However, this fundamental property is a prerequisite in
understanding the electron-phonon coupling of semiconductors. Here we apply
\emph{ab initio} many body perturbation theory to the electron-phonon coupling
on hexagonal silicon carbide (SiC) crystals and determine the temperature
dependence of the bands. We find a significant electron-phonon renormalization
of the band gap at 0~K. Both the conduction and valence bands shift at elevated
temperatures exhibiting a different behavior. We compare our theoretical
results with the observed thermal evolution of SiC band edges, and discuss our
findings in the light of high temperature SiC electronics and defect qubits
operation.
