In recent work, we have suggested that the high-redshift (z∼ 2–4) bright submillimetre galaxy (SMG) population is heterogeneous, with major mergers contributing both at early stages, where quiescently star-forming discs are blended into one submm source (‘galaxy-pair SMGs’), and at late stages, where mutual tidal torques drive gas inflows and cause strong starbursts. Here we combine hydrodynamic simulations of major mergers with 3D dust radiative transfer calculations to determine observational diagnostics that can distinguish between quiescently star-forming SMGs and starburst SMGs via integrated data alone. We fit the far-infrared (FIR) spectral energy distributions of the simulated galaxies with the optically thin single-temperature modified blackbody, the full form of the single-temperature modified blackbody and a power-law temperature distribution model. The effective dust temperature, Td, and power-law index of the dust emissivity in the FIR, β, derived can significantly depend on the fitting form used, and the intrinsic β of the dust is not recovered. However, for all forms used here, there is Td above which almost all simulated galaxies are starbursts, so a Td cut is very effective at selecting starbursts. Simulated merger-induced starbursts also have higher LIR/Mgas and LIR/LFUV than quiescently star-forming galaxies and lie above the star formation rate–stellar mass relation. These diagnostics can be used to test our claim that the SMG population is heterogeneous and to observationally determine what star formation mode dominates a given galaxy population. We comment on applicability of these diagnostics to ultraluminous IR galaxies (ULIRGs) that would not be selected as SMGs. These ‘hot-dust ULIRGs’ are typically starburst galaxies lower in mass than SMGs, but they can also simply be SMGs observed from a different viewing angle.