Colloidal cadmium selenide (CdSe) nanoplatelets (NPLs) are a recently developed class of efficient luminescent nanomaterials suitable for optoelectronic device applications. A change in temperature greatly affects their electronic bandstructure and luminescence properties. It is important to understand how and why the characteristics of NPLs are influenced, particularly at elevated temperatures, where both reversible and irreversible quenching processes come into the picture. Here we present a study of the effect of elevated temperatures on the characteristics of colloidal CdSe NPLs. We used an effective-mass envelope function theory based 8-band k·p model and density-matrix theory considering exciton-phonon interaction. We observed the photoluminescence (PL) spectra at various temperatures for their photon emission energy, PL linewidth and intensity by considering the exciton-phonon interaction with both acoustic and optical phonons using Bose-Einstein statistical factors. With a rise in temperature we observed a fall in the transition energy (emission redshift), matrix element, Fermi factor and quasi Fermi separation, with a reduction in intraband state gaps and increased interband coupling. Also, there was a fall in the PL intensity, along with spectral broadening due to an intraband scattering effect. The predicted transition energy values and simulated PL spectra at varying temperatures exhibit appreciable consistency with the experimental results. Our findings have important implications for the application of NPLs in optoelectronic devices, such as NPL lasers and LEDs, operating much above room temperature.