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The thermal conductivity, lambda, and the specific heat capacity at constant pressure, c_p, have been measured for solid sodium chlorate (NaClO₃) in the temperature range 100-300K. Differential scanning calorimetry (DSC) was used to measure c_p at atmospheric pressure, whilst the transient hot-wire method was used to measure simultaneously both lambda and the heat capacity per unit volume, rho c_p, up to a pressure of 2 GPa. We found that our measured DSC values of c_p exceeded those previously predicted from a lattice dynamical model, consistent with a previous prediction of disorder in Cl atom positions at high temperatures. However, such disorder, if it exists, did not affect the transport of heat, since we found that lambda (T) under isochoric conditions appeared to be determined entirely by three-phonon umklapp interactions. We found no evidence for a phase transition in NaClO₃ up to 2 GPa at 300K, contrary to some previous results. However, we did observe an explosive chemical instability to occur at about 1 GPa and 130K.