We present the first experimental evidence that the heat capacity of superfluid 4He, at temperatures very close to the lambda point Tλ, is enhanced by a constant heat flux Q. The heat capacity at constant Q, CQ, is predicted to diverge at a temperature Tc(Q)<Tλ at which superflow becomes unstable. In agreement with previous measurements, we find that dissipation enters our cell at a temperature, TDAS(Q), below the theoretical value, Tc(Q). We argue that TDAS(Q) can be accounted for by a temperature instability at the cell wall, and is therefore distinct from Tc(Q). The excess heat capacity we measure has the predicted scaling behavior as a function of T and Q, but it is much larger than predicted by current theory
