In contrast to virtually all natural diamonds, synthetic diamonds show a considerable, reversible, change in colour upon heating. This colour change from yellow to reddish brown in the type Ib diamonds is especially noticeable above 500 K and is attributed to the interaction of optical transitions at the substitutional nitrogen impurity centres with lattice vibrations. Optical absorption spectra of homogeneous regions in several crystals were measured as a function of temperature (77-773 K) in the wavelength interval 200-700 nm. The spectra are interpreted in terms of an analytical model for electronic transitions from a deep donor level to a continuous range of levels in the conduction band, where strong electron-phonon coupling is taken into account. Numerical evaluation based on this model yielded a Huang-Rhys factor, S=16+or-1, a phonon energy, h(cross) omega =0.15+or-0.02 eV and the temperature dependence of the nitrogen donor ionization energy. Upon a temperature rise to 750 K the latter showed a decrease of about 0.08 eV.