The Newton-Euler inverse mass operator (NEIMO) method for internal coordinate molecular dynamics (MD) of macromolecules (proteins and polymers) leads to stable dynamics for time steps about 10 times larger than conventional dynamics (e.g., 20 or 30 fs rather than 1 or 2 fs for systems containing hydrogens). NEIMO is practical for large systems since the computation time scales linearly with the number of degrees of freedom N(instead of the N-3 scaling for conventional constrained MD methods). In this paper we generalize the NEIMO formalism to the Nose (and Hoover) thermostat to derive the Nose and Hoover equations of motion for constrained canonical ensemble molecular dynamics. We also examined the optimum mass, Q, determining the time scale (tau(s)) for exchange of energy with the heat bath for NEIMO-Hoover dynamics of polymers. We carried out NEIMO-Hoover simulations on the amorphous polymers poly(vinyl chloride) and poly(vinylidene fluoride), where we find that time steps of 20-30 fs lead to stable dynamics (10 times larger than for Cartesian dynamics). The computational efficiency of the NEIMO canonical MD method should make it a powerful tool for MD simulations of macromolecular materials.