The propagation of domain walls in magnetic microwires has been investigated over the temperature range $77\text{--}373\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Very high domain wall velocities, up to $1800\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s}$, were observed, in combination with enhanced domain wall mobilities at high temperature. In contrast, the domain wall mobility is low at low temperature, though the wires still exhibit relatively high domain wall velocities $(\ensuremath{\sim}600\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s})$. A mechanism for obtaining high wall velocities, based on a negative critical propagation field, is described.