Electron effective mass is a fundamental material parameter defining the free charge carrier transport properties, but it is very challenging to be experimentally determined at high temperatures relevant to device operation. In this work, we obtain the electron effective mass parameters in a Si-doped GaN bulk substrate and epitaxial layers from terahertz (THz) and mid-infrared (MIR) optical Hall effect (OHE) measurements in the temperature range of 38-340 K. The OHE data are analyzed using the well-accepted Drude model to account for the free charge carrier contributions. A strong temperature dependence of the electron effective mass parameter in both bulk and epitaxial GaN with values ranging from (0.18 +/- 0.02) m(0) to (0.34 +/- 0.01) m(0) at a low temperature (38 K) and room temperature, respectively, is obtained from the THz OHE analysis. The observed effective mass enhancement with temperature is evaluated and discussed in view of conduction band nonparabolicity, polaron effect, strain, and deviations from the classical Drude behavior. On the other hand, the electron effective mass parameter determined by MIR OHE is found to be temperature independent with a value of (0.200 +/- 0.002) m(0). A possible explanation for the different findings from THz OHE and MIR OHE is proposed. (c) 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/)