In the explicitly correlated CCSD(T)-F12b coupled cluster method only the singles and doubles component of the energy benefits from inclusion of terms involving the interelectronic distance. Consequently, only that component exhibits accelerated convergence with respect to the 1-particle basis set. The smaller perturbative triples component converges at the same rate as the corresponding piece in standard CCSD(T). With the alternative CCSD(T*)-F12b method the triples correlation energy is scaled up by the ratio of explicitly correlated to standard second-order perturbation theory correlation energies in an attempt to better approximate the basis set limit. An extensive and diverse 212 molecule collection of reference total atomization energies, developed with large basis sets (up to aug-cc-pV9Z in some cases) and standard CCSD(T), was used to calibrate the performance of CCSD(T*). Scaling of the (T) energy led to improved results relative to raw F12b values but only provided a statistical advantage over previously proposed complete basis set extrapolation techniques for the smallest basis sets. With larger sets, scaling (T) produced noticeably poorer results, sometimes by a factor of 2. In agreement with earlier studies, basis set extrapolated CCSD(T)-F12b was found to exhibit a systematic bias toward overestimating reference atomization energies with an error that increases with the magnitude of the valence correlation energy.