The dielectric function [Formula: see text] of monolayer molybdenum diselenide (MoSe2) is obtained and analyzed at temperatures from 31 to 300 K and at energies from 0.74 to 6.42 eV. The sample is a large-area, partially discontinuous monolayer (submonolayer) film of MoSe2 grown on a sapphire substrate by selenization of pulsed laser deposited MoO3 film. Morphological and optical characterizations verified the excellent quality of the film. The MoSe2 data were analyzed using the effective medium approximation, which treats the film and bare substrate regions as a single layer. Second derivatives of ε with respect to energy were numerically calculated and analyzed with standard lineshapes to extract accurate critical-point (CP) energies. We find only 6 CPs for monolayer MoSe2 at room temperature. At cryogenic temperatures 6 additional structures are resolved. The separations in the B- and C-excitonic peaks are also observed. All structures blue-shift and sharpen with decreasing temperature as a result of the reducing lattice constant and electron-phonon interactions. The temperature dependences of the CP energies were determined by fitting the data to the phenomenological expression that contains the Bose-Einstein statistical factor and the temperature coefficient.