This paper explores the microcanonical temperature of an isolated molecule. The molecule is treated as an ensemble of quantum harmonic oscillators, and the temperature is derived in the The discussion tracks the effect of several hypotheses and approximations on the results, including the entropy functional, the type of average frequency, the extension of discrete into continuous variables, the use of Stirling's approximation, the assumption of a large number of degrees of freedom N, and the expansion in the leading orders. T delivers a good approximation for the microcanonical temperature within an error of 3%.