Ok try this,
as dv=0, dU=dQ, dU=CdT=dQ,
dS=CdT/T for both reservoirs with relavant limits,
deltaS=Cln(T/Th)+Cln(T/Tc)=0
=> T/Th=Tc/T
=> T=sqrt(ThTc)=319.26K
I presume my max work theory was ok.
Also while your here, I am getting confused again. I don't know wots wrong...