The parallel solution of the 3D heat conduction equation using PETSc results in errors

[fb77 (François Bouchut)]

I think that you are falling into the trap of varf-on, see

Change of sign in linear part of variational problem (varf vs problem)

solve vSolve(u, v) = a(u, v) + l(v) solves a(u, v) + l(v) = 0 while varf vPb(u, v) = a(u, v) + l(v) solves a(u, v) = l(v), so it is expected that you need to shift the sign in front of the linear form.

For your heat definition you should probably change the sign of the rhs parts:
+int3d(Th)( Cv/dt * Told * Tv )
+int3d(Th)( Joule * Tv )