In this study, we observe avalanche-like electron thermal transport in Heliotron J under plasma conditions that exhibit power degradation to the central electron cyclotron heating (ECH). The newly installed GHz sampling electron cyclotron emission diagnostic allows for the observation of the long-distance radial propagation of electron temperature fluctuations. We find that the electron temperature fluctuations are associated with avalanches, because the Te fluctuations (i) propagate from the core to the edge with a speed comparable to the diamagnetic drift velocity, (ii) exhibit a 1/f power-law scaling in the frequency spectrum and a Hurst exponent close to 1, and (iii) dominate in the ECH deposition location and spread to the edge as the heating power increases. Furthermore, the electron heat avalanches can spread to the scrape off layer region when they are enhanced, i.e., the Te fluctuations correlate with the Dα emission, which also has a frequency spectrum that scales with a 1/f power law.