  The cosmological constant problem is examined by taking an Einstein--scalar
with a Higgs-type potential and scrutinizing the infrared structure induced by
finite temperature effects. A variant optimal perturbation theory is
implemented in the recently proposed quantum-gravitational framework. The
optimized renormalized mass, i.e., the renormalized mass determined by the
variant optimal perturbation theory, of the scalar field turns out to be on the
order of the temperature. This shifts the cosmological constant problem to
compatibility of the consequent perturbative analysis. The compatibility is
guaranteed essentially by renormalization group invariance of physical
quantities. We point out the resummation behind the invariance.
