Temperature, vibrational, and matrix effects on the geometry and hyperfine coupling constants of the methane and ethane radical cations are investigated with a combined quantum mechanics and molecular dynamics technique. Density-functional theory (the B3LYP functional) is implemented as the quantum mechanical method. Results obtained for the methane cation are discouraging. The hyperfine coupling constants (HFCCs) obtained from the simulations are in poor agreement with experimental results. These deficiencies are ascribed to the inadequacy of density-functional theory to describe the potential energy surface in this radical. Results obtained for the ethane radical cation with the identical method are more promising. The HFCCs obtained from the simulations are in better agreement with experimental results obtained at 4 K than those obtained from static, gas-phase calculations, indicating vibrational effects are important for this radical even at low temperatures. Temperature effects on the HFCCs in the ethane radical cation observed experimentally are also well reproduced by the simulations.