Thermonuclear reaction rates are calculated at temperatures consistent with nucleosynthesis conditions in stars and supernovae (109≲T≲1010 K). The cross sections as a function of energy are determined by averaging over a density of compound nuclear states, an individual resonance contribution being represented by the Breit-Wigner formula. The proton and α-particle channel radii are estimated by fitting experimental (p, n) and (α, n) cross sections for nuclei in the mass range 40≲A≲200. The influence of the diffuseness of the nuclear surface on barrier penetration is taken into account by multiplying the square well penetration factors by a ‘reflection factor’ in the manner described by Vogtet al. (1965). Thermonuclear rates calculated by these procedures are compared with sums over experimentally determined resonance strengths for a number of charged-particle reactions involving medium mass nuclei (24≲A≲40).