In this paper, correlations between temperature and kinetics of Trichoderma reesei QM9414 growing on wheat bran are described in terms of glucosamine production, oxygen consumption, and carbon dioxide production. Maximum growth temperature (Tmax) being approximately 314 K, is estimated by measuring the radial growth rate on wheat bran. The value is used in the description of the influence of temperature on the maximum specific growth rate (μmax) and maximum glucosamine (Gmax) level. Both correlations are described with a Ratkowsky-type equation. The highest value of μmax and Gmax are found at approximately 307 K and were 0.154 h−1 and 8.7 mg glucosamine g−1 initial dry matter, respectively. A Gaussian curve is used to describe the influence of temperature on yield factor which varies with a factor of 2 between 293 K and Tmax. The maintenance coefficient is determined to be temperature independent. The observed decline in specific activity, measurable below and above Tmax reflects the sensitivity of the fungus to elevated temperatures. The decline rate increases exponentially above Tmax.