A generalization of the generalized Langevin equation (stochastic dynamics) is introduced in order to model chemical reactions which take place in environments with both density and temperature variations. This phenomenological construction-given the name irreversible generalized Langevin equation (iGLE)-ensures that both the bath and its response to the chosen coordinates of the projected systems are characterized by the same imposed temperature profile. As in the earlier construction, the present generalization does reproduce the generalized Langevin equation in equilibrium and quasi-equilibrium limits. Numerical results indicate surprising behavior when the temperature ramping conditions are fast compared to the solvent response.