The coupled reaction-diffusion equations for temperature and density in a fusion plasma are studied for a particular case, where an increased value of the exponent of the temperature in the expression for the heat source term is used as a model for describing a centrally pronounced heating. For the case considered no equilibrium is obtained, not even an unstable equilibrium. The temperature evolution becomes either a decrease of the temperature profile towards zero or an explosion, depending on a measure (the maximum) of the initial temperature. The effects of temperature and density pinch effects are considered.