When a heat flux Q is applied downward through a sample of 4 He near the lambda transition, the helium self organizes such that the gradient in temperature matches the gravity-induced gradient in T λ. All the helium in the sample is then at the same reduced temperature ε = T-Tλ/Tλ and the helium is said to be in the Self-Organized Critical (SOC) state. We have made the first measurements of the 4He SOC state specific heat, C ∇T(T(Q)). There is no measurable difference between C ∇T and the static zero-gravity 4He specific heat for temperatures between 650 and 250 nK below T λ. Closer to T λ, the specific heat is depressed and reaches a maximum value at 50 nK below T λ. This depression is similar to that predicted theoretically as reported by R. Haussmann (Phys. Rev. B 60, 12349, 1999). Contrary to the expectations of theory, however, we see another de pression far below T λ. In addition, over the heat flux range of 30 nW/cm 2 to 13 μW/cm 2, we have made improved measurements of the speed of a recently discovered propagating thermal mode, which travels only upstream against the nominal heat flux of the SOC state. We are able to accurately predict the speed of this wave by treating the helium of SOC state as a traditional fluid with a temperature dependent thermal conductivity.