Binary fluid mixtures with a negative separation ratio heated from below exhibit steady spatially localized states called convectons for supercritical Rayleigh numbers. With no-slip, fixed-temperature, no-mass-flux boundary conditions at the top and bottom stationary odd- and even-parity convectons fall on a pair of intertwined branches connected by branches of travelling asymmetric states. In appropriate parameter regimes the stationary convectons may be stable. When the boundary condition on the top is changed to Newton’s law of cooling the odd-parity convectons start to drift and the branch of odd-parity convectons breaks up and reconnects with the branches of asymmetric states. We explore the dependence of these changes and of the resulting drift speed on the associated Biot number using numerical continuation, and compare and contrast the results with a related study of the Swift–Hohenberg equation by Houghton & Knobloch (Phys. Rev. E, vol. 84, 2011, art. 016204). We use the results to identify stable drifting convectons and employ direct numerical simulations to study collisions between them. The collisions are highly inelastic, and result in convectons whose length exceeds the sum of the lengths of the colliding convectons.