In this article we propose a new approximation for incorporating tunneling into variational transition state theory when the critical degrees of freedom are coupled to a bath. The new approximation is based on a canonically averaged mean-shape potential which can be evaluated from the bath contribution to the potential of mean force as a function of temperature. The new approximation is applied to a polyatomic organic reaction in which some low-frequency modes are treated as a bath and to a model reaction in solution.