To investigate the effects of friction, propellant gas, and projectile jacket materials on the bore temperature evolution during the firing process, a thermo-mechanical coupled finite element model (FEM) was developed for a small-caliber rifle. The model integrated multi-mechanism heat transfer theory, considering the frictional heating at the projectile-barrel interface, the thermal-pressure load from the propellant gas, and the nonlinear temperature-dependent thermophysical properties of the materials. Numerical simulations were conducted to analyze the temperature distribution and evolution in the bore of the barrel. Three loading conditions were modeled to evaluate the contributions of friction and propellant gas effects on the temperature distribution. The results show that the propellant gas is the dominant heat source, significantly increasing the overall barrel temperature, while frictional heating mainly affects localized temperature rises. In the propellant-gas-only model, the maximum land and groove temperatures reach to 574.8 K and 442.0 K, respectively, whereas in the friction-only model, these values were 535.7 K and 320.0 K. Furthermore, the thermal responses of the barrel when firing copper and copper-clad steel jacketed projectiles were compared. Although firing the copper-jacketed projectile generated about 80 % more frictional heat, the barrel experienced lower peak temperatures due to copper's higher thermal conductivity, as well as material detachment of the copper jacket that enhanced heat dissipation. The findings can help understand the bore temperature evolution and barrel thermal damage mechanisms during the interior ballistics process.