We study the far infrared (60-500 $mu$m) colours of late-type galaxies in the $Herschel$ Reference Survey, a K-band selected, volume limited sample of nearby galaxies. The far infrared colours are correlated with each other, with tighter correlations for the indices that are closer in wavelength. We also compare the different colour indices to various tracers of the physical properties of the target galaxies, such as the surface brightness of the ionising and non-ionising stellar radiation, the dust attenuation and the metallicity. The emission properties of the cold dust dominating the far infrared spectral domain are regulated by the properties of the interstellar radiation field. Consistent with that observed in nearby, resolved galaxies, our analysis shows that the ionising and the non-ionising stellar radiation, including that emitted by the most evolved, cold stars, both contribute to the heating of the cold dust component. This work also shows that metallicity is another key parameter characterising the cold dust emission of normal, late-type galaxies. A single modified black body with a grain emissivity index $beta$=1.5 better fits the observed SPIRE flux density ratios $S250/S350$ vs. $S350/S500$ than $beta$=2, although values of $beta$ $simeq$ 2 are possible in metal rich, high surface brightness galaxies. Values of $beta$ $lesssim$ 1.5 better represent metal poor, low surface brightness objects. This observational evidence provides strong constraints for dust emission models of normal, late type galaxies.
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