Using direct numerical simulations (DNS) and large-eddy simulations (LES) of velocity and passive scalar in isotropic turbulence (up to 5123 grid points), we examine directly and quantitatively the refined similarity hypotheses as applied to passive scalar fields (RSHP) with Prandtl number of order one. Unlike previous experimental investigations, exact energy and scalar dissipation rates were used and scaling exponents were quantified as a function of local Reynolds number. We first demonstrate that the forced DNS and LES scalar fields exhibit realistic inertial-range dynamics and that the statistical characteristics compare well with other numerical, theoretical and experimental studies. The Obukhov–Corrsin constant for the k−5/3 scalar variance spectrum obtained from the 5123 mesh is 0.87±0.10. Various statistics indicated that the scalar field is more intermittent than the velocity field. The joint probability distribution of locally-averaged energy dissipation εr and scalar dissipation χr is close to log-normal with a correlation coefficient of 0.25±0.01 between the logarithmic dissipations in the inertial subrange. The intermittency parameter for scalar dissipation is estimated to be in the range 0.43≈0.77, based on direct calculations of the variance of lnχr. The scaling exponents of the conditional scalar increment δrθ[mid ] χr,εr suggest a tendency to follow RSHP. Most significantly, the scaling exponent of δrθ[mid ] χr,εr over εr was shown to be approximately −⅙ in the inertial subrange, confirming a dynamical aspect of RSHP. In agreement with recent experimental results (Zhu et al. 1995; Stolovitzky et al. 1995), the probability distributions of the random variable βs = δrθ[mid ] χr,εr/ (χ1/2r ε−⅙rr1/3) were found to be nearly Gaussian. However, contrary to the experimental results, we find that the moments of βs are almost identical to those for the velocity field found in Part 1 of this study (Wang et al. 1996) and are insensitive to Reynolds number, large-scale forcing, and subgrid modelling.