A hyperelastic-viscoplastic constitutive model for amorphous polymers was used in finite element simulations of micro-hot embossing across the glass transition. The model was selected for its ability to capture finite strain temperature and rate dependence over a wide range of temperatures, including across the glass transition. The simulations focused on the glass transition temperature regime, and particularly probed the effects of time and temperature during cooling and mold release. The results show that strong temperature sensitivity of the material across the glass transition leads to a wide range of required embossing force and springback. The interplay between changes in material properties upon cooling and stress relaxation can lead to significant increases in embossing force during the cooling stage, especially when high cooling rates are employed. The effects of thermal expansion also complicate the problem during rapid cooling. Nonlinear material behavior is shown to affect results in parametric hot embossing studies. Careful tailoring of embossing temperature, cooling rate, and demolding temperature is critical in acceptable feature replication. The best results are found for moderate cooling rates, which allow adequate time for stress relaxation in the material prior to mold release. POLYM. ENG. SCI., 49:531543, 2009. (c) 2009 Society of Plastics Engineers