Measurements of the electron heat diffusivity χ of the JET plasma in a wide variety of discharge conditions are reported. χ is deduced from heat pulse propagation analysis, using the sawtooth collapse as the perturbation of the temperature profile. The measurements of the electron temperature are performed with a 12-channel ECE polychromator. In limiter discharges, scans of plasma current, density, input power and Zeff have been studied. It is shown that χ is independent of density and input power, while a clear dependence on Zeff and on the electron temperature Te is demonstrated. The scaling provides a good fit to the JET data. xhp denotes the normalized radius where χ is measured. This radius is coupled to qa. As a result, the xhp-dependence only parameterizes the combined effect of the plasma current and the profile shapes of temperature, density, safety factor, etc. Various transport models are discussed in the light of this scaling. Also, χ measurements in the Ohmic, L-mode and H-mode phases of X-point plasmas are reported. The χ values are on average 20% higher in the H-mode than in the Ohmic phase. In one discharge where χ was measured in all three phases, no significant changes could be demonstrated.