Earthquakes i.e. frictional ruptures, are commonly described by singular solutions of shear crack motions. These solutions assume a square root singularity order around the rupture tip and a constant shear stress value behind it, implying scale-independent edge-localized energy. However, recent observations of large-scale thermal weakening accompanied by decreasing shear stress potentially affecting the singularity order can challenge this assumption. In this study, we replicate earthquakes in a laboratory setting by conducting stick-slip experiments on PMMA samples under normal stress ranging from 1 to 4 MPa. Strain gauges rosettes, located near the frictional interface, are used to analyze each rupture event, enabling the investigation of shear stress evolution, slip velocity, and material displacement as a function of distance from the rupture tip. Our analysis of the rupture dynamics provides compelling experimental evidence of frictional rupture driven by enhanced thermal weakening. The observed rupture fronts exhibit unconventional singularity orders and display slip-dependent breakdown work (on-fault dissipated energy). Moreover, these findings elucidate the challenges associated with a priori estimating the energy budget controlling the velocity and final extent of a seismic rupture, when thermal weakening is activated during seismic slip.