The existence of an electron heat pinch has been experimentally investigated in ASDEX-Upgrade in plasmas with strong off-axis electron cyclotron heating (ECH). Localization of 1.6MW of ECH power at ρdep = 0.65 in plasmas with low Ohmic power (<100 kW) still resulted in peaked electron temperature (Te) profiles at densities ne0 ∼ 2.7 × 1019 m−3. Two out of four gyrotrons were modulated in order to study convective effects also on the Te transient response at different frequencies. Peculiar profiles of the modulation amplitude have been measured, very flat in the region just inside ρdep (0.3 < ρtor < 0.65) or even increasing rather than decreasing away from ρdep on the inner side. The phase profiles instead regularly indicate the propagation of the heat wave in both directions away from ρdep. Power balance analysis shows that the heat flux in the core region is very close to zero, but uncertainties do not allow a clear determination of its sign. Modelling steady-state and modulation results with an empirical model featuring a diffusive term characterized by a critical gradient length (LTe = −Te/∇Te) behaviour and a constant Gaussian shaped heat pinch profile allows good reproduction of the data when the region just inside ρdep is close to the critical threshold and oscillates around it, and a small convective term U ∼ 1–2ms−1 is present in the same region. At higher density the Te profile becomes flatter and the amplitude profiles recover the usual shape with stronger decay inside with respect to outside ρdep. In this case no heat pinch is needed and the plasma goes below the critical threshold inside ρdep. The results are consistent with the theoretical prediction of a turbulence regulated by a threshold in R/LTe and a small turbulence generated electron heat pinch term. However initial attempts to perform first principle-based simulations using the quasi-linear electrostatic drift waveWeiland model have failed to reproduce the experimental results.