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The role of thermal effects in the focused electron beam induced deposition (FEBID) process of Me$_2$Au(tfac) is studied by means of irradiation-driven molecular dynamics simulations. The FEBID of Me$_2$Au(tfac), a commonly used precursor molecule for the fabrication of gold nanostructures, is simulated at different temperatures in the range of $300-450$ K. The deposit's structure, morphology, growth rate, and elemental composition at different temperatures are analyzed. The fragmentation cross section for Me$_2$Au(tfac) is evaluated on the basis of the cross sections for structurally similar molecules. Different fragmentation channels involving the dissociative ionization (DI) and dissociative electron attachment (DEA) mechanisms are considered. The conducted simulations of FEBID confirm experimental observations that deposits consist of small gold clusters embedded into a carbon-rich organic matrix. The simulation results indicate that accounting for both DEA- and DI-induced fragmentation of all the covalent bonds in Me$_2$Au(tfac) and increasing the amount of energy transferred to the system upon fragmentation increase the concentration of gold in the deposit. The simulations predict an increase in Au:C ratio in the deposit from 0.18 to 0.25 upon the temperature increase from 300 K to 450 K, being within the range of experimentally reported values., 14 pages, 8 figures