We study the effect of a stationary heat current Q on superfluid He-4
in a homogeneous metastable state near T(lambda)(Q). On the basis of a
renormalization-group calculation we predict a sizable enhancement of
the specific heat C(P)(Q) and a weak depression of the superfluid den
sity rho(s)(Q) up to a critical heat current Q(c)(T) where C(P) and rh
o(s) exhibit cusplike anomalies.