The equations of one-dimensional heat transfer with chemical reactions with isothermal initial conditions and constant wall temperature are solved approximately for all types of kinetic models. The general solution is valid for low exothermal peaks and it is characterized explicitly by two dimensionless parameters. The first parameter is the ratio between the time scale for heat conduction and that for the chemical reaction; the second parameter is the ratio between the processing temperature and the adiabatic temperature rise. The number of additional parameters depends on the particular choice of kinetic model. The maximum temperature in the solution always occur at the center line and its magnitude is proportional to the maximum rate of reaction. For a second-order autocatalytic kinetic model, closed form results can be obtained. The solution is in this case characterized by two additional dimensionless parameters. The analytical solution agrees excellently with numerical solutions for small exothermal temperature peaks (< 10% of the adiabatic temperature rise), but the qualitative agreement is very good also for cases with significant exothermal peaks. The general solution can be used also for the case when the kinetic model is unknown and only experimental DSC results are available.