  A holonomic constraint is used to enforce a constant instantaneous
configurational temperature on an equilibrium system. Three sets of equations
of motion are obtained, differing according to the way in which the holonomic
constraint is introduced and the phase space distribution function that is
preserved by the dynamics. Firstly, Gauss' principle of least constraint is
used, and it is shown that it does not preserve the canonical distribution.
Secondly, a modified Hamiltonian is used to find a dynamics that provides a
restricted microcanonical distribution. Lastly, we provide equations that are
specifically designed to both satisfy the temperature constraint and produce a
restricted canonical ensemble.
