  The investigation of symmetry nonrestoration scenarios has led to a
controversy, with certain nonperturbative approximation schemes giving
indications in sharp disagreement with those found within conventional
perturbation theory. A Rayleigh-Ritz variational approach to the problem, which
might be useful in bridging the gap between perturbative and nonperturbative
viewpoints, is here proposed. As a first application, this approach is used in
the investigation of a $Z_2 \times Z_2$-invariant thermal field theory with two
scalar fields, placing particular emphasis on the region of parameter space
that has been claimed to support symmetry nonrestoration.
