Heat dissipation is a natural consequence of operating any electronic system. In nearly all computing systems, such heat is usually minimized by design and cooling. Here, we show that the temporal dynamics of internally produced heat in electronic devices can be engineered to both encode information within a single device and process information across multiple devices. In our demonstration, electronic NbOx Mott neurons, integrated on a flexible organic substrate, exhibit 18 biomimetic neuronal behaviours and frequency-based nociception within a single component by exploiting both the thermal dynamics of the Mott transition and the dynamical thermal interactions with the organic substrate. Further, multiple interconnected Mott neurons spatiotemporally communicate purely via heat, which we use for graph optimization by consuming over 106 times less energy when compared with the best digital processors. Thus, exploiting natural thermal processes in computing can lead to functionally dense, energy-efficient and radically novel mixed-physics computing primitives.