The TESLA 9-cell SRF cavity design has been adopted for use in the LCLS-II SRF Linac. Its TTF3 coaxial fundamental power coupler (FPC), optimized for pulsed operation in European XFEL and ILC, requires modest changes to make it suitable for LCLS-II continuous-wave (CW) operation. For LCLS-II it must handle up to 7 kW of power, fully reflected, with the maximum temperature around 450 K, the coupler bake temperature. In order to improve TTF3 FPC cooling, an increased copper plating thickness will be used on the inner conductor of the ?warm? section of the coupler. Also, the antenna will be shortened to achieve higher cavity Qext values. Fully 3D FPC thermal analysis has been performed using the SLAC-developed parallel finite element code suite ACE3P, which includes electromagnetic codes and an integrated electromagnetic, thermal and mechanical multi-physics code. In this paper, we present TTF3 FPC thermal analysis simulation results obtained using ACE3P as well as a comparison with measurement results.