Abstract:Optical systems have been pivotal for energy-efficient computing, performing high-speed, parallel operations in low-loss carriers. While these predominantly analog optical accelerators bypass digitization to perform parallel floating-point computations, scaling optical hardware to map large-vector sizes for AI tasks remains challenging. Here, we overcome this limitation by unfolding scalar operations in time and introducing a photonic-heater-in-lightpath (PHIL) unit for all-optical temporal integration. Counterintuitively, we exploit a slow heat dissipation process to integrate optical signals modulated at 50 GHz bridging the speed gap between the widely applied thermo-optic effects and ultrafast photonics. This architecture supports optical end-to-end signal processing, eliminates inefficient electro-optical conversions, and enables both linear and nonlinear operations within a unified framework. Our results demonstrate a scalable path towards high-speed photonic computing through thermally driven integration.