The unsteady evolution of a boundary layer induced by a rectilinear vortex convecting above a heated surface is considered numerically. This model problem is representative of the types of interactions that can occur when vortices encounter solid surfaces in a wide variety of diverse applications involving high-Reynolds-number and high-Grashof-number flows. It is known that in the case without heat transfer, the vortex-induced boundary layer evolves toward a singularity as it forms a sharp spike that erupts away from the surface. Numerical solutions of the unsteady mixed-convection boundary-layer equations in the Boussinesq limit are obtained in Lagrangian coordinates. Solutions for various values of the inclination angle of the surface and Grashof number show that the coupling between the fluid flow and heat transfer can have a dramatic effect upon the transport of momentum and energy within the boundary layer induced by the vortex. The unsteady eruption convects high-temperature, near-wall fluid away from the surface and causes large gradients in the thermal boundary layer. The buoyancy force acting on the heated boundary-layer fluid can also have a significant impact on the unsteady separation process, either accelerating or delaying it, depending upon the inclination angle of the surface.