ABSTRACT 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 ∼1800 spectra obtained by Rossi X-Ray Timing Explorer Proportional Counter Array 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 multicolour disc model DISKBB yields significantly lower and often unphysical inner disc radii and correspondingly higher (∼50–60 per cent) disc temperatures compared to its relativistic counterparts KYNBB and KERRBB. We obtained the dimensionless spin parameters of a* = 0.774 ± 0.069 and a* = 0.752 ± 0.061 for GRO J1655−40 with KERRBB and KYNBB, respectively. We report a spin value of a* = 0.098 ± 0.063 for LMC X-3 using the updated black hole mass of 6.98 M⊙. 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.