All-optical magnetic switching (AOS) is a recently observed rich and puzzling phenomenon that offers promising technological applications. However, a fundamental understanding of the underlying mechanisms remains elusive. Here we present a model for multishot helicity-dependent AOS in ferromagnetic materials based on a purely heat-driven mechanism in the presence of magnetic circular dichroism (MCD). We predict that AOS should be possible with as little as 0.5% of MCD, after a minimum number of laser shots heat the sample close to the Curie temperature. Finally, we qualitatively reproduce the all-optically switched domain patterns observed experimentally by numerically simulating the result of multiple laser shots on an FePtC granular ferromagnetic film.