Rapid sliding rigid indentation with friction of a half-space is analyzed as a two-dimensional steady-state process governed by fully coupled thermoelasticity. While rapid sliding justifies an insulated contact zone, the half-space surface outside the zone is allowed to (i) exchange heat with the atmosphere via convection and (ii) have its convective properties altered by the sliding process itself. The problem boundary conditions are mixed in both mechanical and thermal fields, yet robust asymptotic forms are used to reduce analysis to a simply coupled integral equation set that exhibits both Abel and Cauchy operators. Exact solutions show that convection has no influence on contact zone extent, although other thermoelastic parameters do. The surface temperature, however, is both controlled by friction and influenced by convection; effects of the latter are even more pronounced far away from the indentor.