Hughes etal. (1993) have made submillimetre continuum observations of 10 IRAS selected radio-quiet quasars (RQQs). Three RQQs, I Zw 1, Mrk1014 and Mrk376, have been detected at 800 and 450μm using the 3He bolometer UKT14 on t he 15-m James Clerk Maxwell telescope. These submillimetre data, together with existing 1.3 mm observations (Chini etal. 1989) demonstrate that the measured submillimetre spectral indices, 〈αsm〉 = 3.8 ± 0.5, significantly exceed the critical theoretical limit of αsm = 2.5 predicted for the self-absorption of synchrotron emission. This result is independent of any contributions to the 100μm IRAS fluxes from cirrus emission in the host galaxies, extended circumnucl ear starformation and FIR emission from companion or confusing sources. All current non-thermal models (de Kool & Begelman 1989, Schlickeiser etal. 1991) are rejected in favour of the alternative explanation that the FIR luminosity is dominated by thermal emission from warm (45–60 K) dust grains. The submillimetre optical depth and source-size for the thermal emission cannot yet be constrained by these data and, as a result, no discrimination can be made between dust heated by an extended (> 1 kpc) starburst region or a central compact luminosity source. However ground-based imaging observations at mid-IR wavelengths and FIR photometry (60–200μm) with the KAO are currently in progress specifically to address this problem. The high gas masses (> 1010M⊙) in RQQs inferred from the submillimetre continuum observations are in agreement with the H2 masses determined from CO measurements. Alternatively the results show that the MH2/Mdust ratio measured in RQQs (∼ 370 ± 150) is consistent with that measured in spiral galaxies and ultra-luminous IRAS galaxies.