Thanks for taking the time to respond and analyze my comment! - The bigger the slope (in space), the faster (in time) the temperature changes at that point - I

Thanks for taking the time to respond and analyze my comment! - The bigger the slope (in space), the faster (in time) the temperature changes at that point - I have to confess that I got it wrong, indeed: the right side of the equation is a Laplacian. But, rather than describing an average in temperature, it describes the divergence of the temperature field.