  Black hole X-ray binaries are ideal environments to study the accretion
phenomena in strong gravitational potentials. These systems undergo dramatic
accretion state transitions and analysis of the X-ray spectra is used to probe
the properties of the accretion disc and its evolution. In this work, we
present a systematic investigation of $\sim$1800 spectra obtained by RXTE PCA
observations of GRO J1655-40 and LMC X-3 to explore the nature of the accretion
disc via non-relativistic and relativistic disc models describing the thermal
emission in black-hole X-ray binaries. We demonstrate that the non-relativistic
modelling throughout an outburst with the phenomenological multi-colour disc
model DISKBB yields significantly lower and often unphysical inner disc radii
and correspondingly higher ($\sim$50-60\%) disc temperatures compared to its
relativistic counterparts KYNBB and KERRBB. We obtained the dimensionless spin
parameters of $a_{*}=0.774 \pm 0.069 $ and $a_{*}=0.752 \pm 0.061 $ for GRO
J1655-40 with KERRBB and KYNBB, respectively. We report a spin value of
$a_{*}=0.098 \pm 0.063$ for LMC X-3 using the updated black hole mass of 6.98
${M_{\odot}}$. Both measurements are consistent with the previous studies.
Using our results, we highlight the importance of self-consistent modelling of
the thermal emission, especially when estimating the spin with the
continuum-fitting method which assumes the disc terminates at the innermost
stable circular orbit at all times.
