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tokens: per degree of freedom lies in the range 0.4–3.0 increases from 1098 to 1123 when fitting this simpler model. We therefore proceed in the knowledge that the excess rest-frame 1–3 μ m emission in our sample of quasars can be adequately described using a fixed temperature blackbody in our SED model, consistent with emission from dust at its sublimation temperature (e.g. Barvainis 1987 ). However, we ascribe no further significance to the exact value of this temperature, noting instead that it is merely the temperature describing the blackbody which best describes the infrared colours of the quasars, and not necessarily the exact physical temperature of the emitting dust. In particular, we note that this temperature is degenerate with the slope of the power-law continuum (−1.84) which we assume in our model, and a different continuum slope would lead to a slightly different hot dust temperature. Our subsequent results would be qualitatively unchanged. 3.4 Primary sample Fixing the blackbody temperature allows us to fit our model to higher redshift objects, where we no longer have two independent data points probing the hottest dust emission. For what we hereafter refer to as our ‘primary’ sample, we take all quasars in the redshift range 1.2 z 2.0 (see Appendix D for a discussion of the limitations of higher redshift objects). For our primary sample, the W2 band probes rest-frame wavelengths ≈2 μ m where the hot dust blackbody is expected to be the dominant contributor to the total flux. We require detections in all of the JKW12 bands. To avoid biases against hot-dust-faint objects which might drop out of one or more of these bands we restrict our primary sample to Y 19.3, where the sample is better than 95 per cent complete in all UKIDSS bands, giving a total of 12 294 objects. We have verified that restricting our sample to a brighter flux limit does not change any of the subsequent results. When constructing the sample, only 243 objects are lost due to missing unWISE data, meaning our primary sample is more than 98 per cent complete in W1 and W2 . Some of these objects will be missed due to crowded fields as the WISE point spread function is significantly broader than that of SDSS. However, we cannot rule out the possibility that a small fraction of objects are lost due to intrinsically faint fluxes in the rest-frame near-infrared. We fit our primary sample with two free parameters in the model, fixing T blackbody = 1280 K and allowing just the E ( B − V ) and normalization of the hot dust component to vary. The median χ 2 per degree of freedom when fitting our model to this sample is 1.30. We show in Appendix E that our subsequent results remain unchanged when instead using a hotter or cooler blackbody in our model quasar SED. 5022 objects from our primary sample with z > 1.56 also have C iv line information from Rankine et al. ( 2020 ). As the sample is restricted to z 2.0, Mg ii emission is present in the SDSS spectra to enable black hole