Abstract: A heatbath algorithm is proposed for pure SU(𝑁) lattice gauge theory based on the Manton action of the plaquette element for general gauge group 𝑁. Comparison is made to the Metropolis thermalization algorithm using both the Wilson and Manton actions. The heatbath algorithm is found to outperform the Metropolis algorithm in both execution speed and decorrelation rate. Results, mostly in 𝐷 =3, for 𝑁 =2 through 5 at several values for the inverse coupling are presented.