It is known that rapid edge cooling of magnetically confined plasmas can trigger heat pulses that propagate rapidly inward. These can result in large excursion, either positive or negative, in the electron temperature at the core. A set of particularly detailed measurements was obtained in Large Helical Device(LHD) plasmas [S. Inagaki et al, Plasma Phys. Control. Fusion 52 (2010) 075002], which are considered here. By applying a travelling wave transformation, we extend the model of R. O. Dendy, S. C. Chapman and S. Inagaki, Plasma Phys. Control. Fusion 55 (2013) 115009, which successfully describes the local time-evolution of heat pulses in these plasmas, to include also spatial dependence. The new extended model comprises two coupled nonlinear first order differential equations for the (x; t) evolution of the deviation from steady state of two independent variables: the excess electron temperature gradient and the excess heat flux, both of which are measured in the LHD experiments. The mathematical structure of the model equations implies a formula for the pulse velocity, defined in terms of plasma quantities, which aligns with empirical expectations and is within a factor of two of the measured values. We thus model spatio-temporal pulse evolution, from first principles, in a way which yields as output the spatiotemporal evolution of the electron temperature, which is also measured in detail in the experiments. We compare the model results against LHD datasets using appropriate initial and boundary conditions. Sensitivity of this nonlinear model with respect to plasma parameters, initial conditions and boundary conditions is also investigated. We conclude that this model is able to match experimental data for the spatio-temporal evolution of the temperature profiles of these pulses, and their propagation velocities, across a broad radial range from r=a ' 0:5 to the plasma core. The model further implies that the heat pulse may be related mathematically to soliton solutions of the Korteweg-de Vries-Burgers equation.