We present a detailed investigation of X-ray spectral models used to fit the thermal accretion disc emission in black-hole X-ray binaries. To explore the nature of the accretion disc in strong gravitational fields via non-relativistic and relativistic disc models, we fit ~2000 RXTE observations of GRO J1655-40 and LMC X-3. We find that the non-relativistic multi-colour disc blackbody model (diskbb) gives significantly (about ~50-60%) higher values for disc temperatures and lower (often unphysical) inner disc radii than relativistic disc models. We find that this difference in the disc temperature and inner disc radius cannot be explained by only varying spectral hardening factor and varying inner disc radius in combination with relativistic treatment of the disc is a more probable explanation for the previously reported deviations in the L-T relationship in a subset of black hole X-ray binaries. Our study clearly shows the importance of self-consistent modeling of the thermal emission in accreting compact objects, especially when estimating the black hole spin with the continuum-fitting method.