We present low-temperature thermal conductivity measurements on the cuprate Tl2Ba2CuO6+delta throughout the overdoped regime. In the T -> 0 limit, the thermal conductivity due to d-wave nodal quasiparticles provides a bulk measurement of the superconducting gap Delta. We find Delta to decrease with increasing doping, with a magnitude consistent with spectroscopic measurements (photoemission and tunneling). This argues for a pure and simple d-wave superconducting state in the overdoped region of the phase diagram, which appears to extend into the underdoped regime down to a hole concentration of similar or equal to 0.1 hole/Cu. As hole concentration is decreased, the gap-to-T-c ratio increases, showing that the suppression of the superconducting transition temperature T-c (relative to the gap) begins in the overdoped regime.