Acoustically driven bubbles are nonlinear oscillators showing a wide range of behaviors such as period-doubling bifurcations, deterministic chaos, and synchronization to an external signal. Here we demonstrate that bubbles driven with a constant heat source can couple with each other and yield in-phase synchronization, even in the absence of an external sound field. Besides perfect synchronization, we resolve the parameter space where independent oscillations and bubble merging occur. The main finding that only weakly driven oscillating bubbles synchronize provides a path for experimental scale-up to study spatiotemporal synchronization. In the wider scope the findings are relevant for heat transfer applications from structured heaters where complex multibubble oscillations are expected.