This paper investigates the impact of channel geometry on the selfheating temperature of a 10 nm gate-length GaAs-based gate-all-around fieldeffect transistor (GAAFET). The study is conducted using numerical simulations in the Sentaurus TCAD environment. While maintaining a constant channel crosssectional area, the channel height is varied from 12 nm to 4 nm, resulting in a corresponding change in channel width. The simulation results demonstrate that reducing the channel height increases the drain current and affects the temperature distribution within the transistor. It is observed that for channel heights below 6 nm, enhanced heat dissipation through the enlarged external surface area dominates Joule heat generation, leading to a reduction in the peak self-heating temperature. These findings provide valuable insights for optimizing nanoscale GaAs GAAFET designs with improved thermal performance.