Theory suggests that thermocapillary flow about neighboring bubbles in liquids on hot walls pulls the bubbles together. A temperature gradient perpendicular to the wall establishes a surface tension gradient at the bubble-liquid interface, which in turn sustains a shear stress gradient that pumps adjacent fluid away from the wall. Neighboring bubbles are mutually entrained in this how and also respond thermophoretically to lateral temperature gradients in the temperature near field. The theory predicts that the aggregation velocity scales with the temperature gradient, the radius of the bubbles, the derivative of the surface tension with respect to temperature, and the reciprocal of the liquid's viscosity. Bubble aggregation experiments under controlled conditions were performed to test the theory. Scaling the experimental bubble trajectories according to the theory substantially collapses all of the data onto a master curve when the interbubble separation is greater than 3 radii, which suggests that the theory is correct. Calculated velocities agree with the experimental results when hindrance of bubble motion due to the wall is included. Values for the parameter that describes the hindrance effect are obtained from fitting the data to the theory, from independent measurements, and from direct hydrodynamic calculation. The results of the three determinations agree within 15% of the possible range of the value of the parameter.