  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.
