Heat generation and conduction at moving interfaces are ubiquitous and fundamentally important. However, despite decades of progress on thermal transport across static interfaces, insights into moving interfaces remain rare due to the complex and ever-changing nature of most sliding contacts. Here, we take advantage of structural superlubricity and achieve simultaneous mechanical manipulation and thermal measurement of the heterointerface between gold micro mesas and single-crystalline graphite. We uncover a robustly high thermal conductance which is orders of magnitude higher than that in conventional moving contacts and remarkably insensitive to arbitrary interfacial rotation and thousands of cycles of sliding. In conjunction with atomistic simulations, we reveal the critical role of full atomic contact associated with the interfacial superlubricity and the stacking-insensitive out-of-plane phonon modes that dominate heat transfer. Altogether, our findings highlight diverse superlubric heterointerfaces as a pristine platform for exploring phonon dynamics in moving systems and managing heat in emerging devices including twistronics and slidetronics.