Rare-events molecular dynamics techniques are used to study the interconversion between the two half-chair isomers of cyclohexene (C6H10), in a solvent modelled through a stochastic bath, in order to investigate dynamic solvent effects on the isomerization rate. Adopting the torsional angle around the C-C sigma bond opposite to the double bond as the reaction coordinate, we calculate the equilibrium distribution of this coordinate (using umbrella sampling), and estimate the isomerization rate, including the transmission coefficient κ. The paper also contains methodological developments. A variant of Andersen's stochastic collision method (canonical ensemble sampling) is developed for molecules with constraints: by resampling Cartesian velocities of a localized subgroup of atoms of the molecule and leaving all other atomic velocity components unchanged, one mimics the collision of a virtual gas molecule with a subpart of the molecule of interest. To evaluate the transmission coefficient κ, the initial conditions for trajectories ‘crossing the top’ are automatically generated during the run, using a biased potential to obtain the probability of being at the saddle point.