We characterize how film thickness affects the thermomechanical response of free-standing nanofilms composed of a thermoset polymer, diglycidyl ether of Bisphenol A (DGEBA) with 3,3'-diaminodiphenyl sulfone (33DDS), via molecular dynamics. We find that the glass transition temperature, Young's modulus, and yield stress of the films decrease with decreasing thickness with the later two properties deviating from their bulk values at slightly larger thicknesses. The relative role of (i) intrinsic size effects, (ii) changes in quench depth (T - T(g)), and (iii) variability in curing degree, on the depression of mechanical response of ultrathin films, are quantified. We find that intrinsic size effects contribute over 60% of the total change in mechanical response for the entire range of thicknesses studied.