We present the mesoscopic description of stochastic effects in a thermochemical bistable diluted gas system subject to the Newtonian heat exchange with a thermostat. We apply the master equation including a transition rate for the Newtonian thermal transfer process, derived on the basis of kinetic theory. As temperature is a continuous variable, this master equation has a complicated integro-differential form. We perform Monte Carlo simulations based on this equation to study the stochastic effects in a homogeneous Semenov model (which neglects reactant consumption) in the bistable regime. The mean first passage time is computed as a function of the number of particles in the system and the distance from the bifurcation associated with the emergence of bistability. An approximate analytical prediction is deduced from the Fokker--Planck equation associated with the master equation. The results of the master equation approach are successfully compared with those of direct simulations of the microscopic particle dynamics.

PACS numbers: 05.10.Gg, 82.33.Vx, 05.10.Ln, 82.20.Wt