The propagation of heat pulses originating from sawtooth activity in JET has been investigated in a series of limiter discharges with the parameters IP ~ 3MA. BT ~ 3T. k = 1.45. The auxiliary power was varied, so that the total power ranged from 2 to 13.5MW. Electron temperature perturbations in a 20cm region around a minor radius r = 2/3 a. were recorded with high time resolution. using a 12 channel Electron Cyclotron Emission (ECE) polychromator. From these measurements the electron heat diffusivity ceHP was derived. Over the the whole range of powers considered. χeHPwas found to be independent of power and to lie in the range 2.5±0.5m2/s. We compare χeHP to χeGLO derived from global power balance analysis. For ohmic heating the latter is lower than χeHP by a factor 2.5. For increasing auxiliary power, χeGLO approaches χeHP. We present a model for the dependence of the local χe on the temperature gradient, which permits a unified description of the heat pulse bebaviour, the deterioration of confinement and a certain degree of profile consistency. The model does not invoke non-local parameters like the total power input. It is shown that the present heat pulse data contradicts τE-scaling laws of the typical form τE÷P-0 .5.