Analytic approximations to relativistic plasma dispersion functions are derived in terms of the exponential integral function, ${\rm Ei}(x)$, for relativistic temperatures $T\gapprox m_{\rm e}c^2$ (where $m_{\rm e}c^2$ is the electron rest energy). It is shown that a simpler, useful approximation to these functions can be obtained based on known approximations to the exponential integral function.