excess thrust the same, so rate of climb the same
Nope, fell at the last unfortunately! Excess thrust at higher speed generates more power, and therefore a higher
rate of climb -- just enough, in fact, to compensate for the extra distance travelled and make the gradient of climb the same.
If you take it from the basic equations for equilibrium,
T - D = L*tan(angle_of_climb)
So the angle of climb ends up depending on (T - D)/L
D/L is (near enough) the same at the same CAS, so the angle of climb ends up depending on thrust available.
I know very little about turbine engines, but is the assumption that the thrust is flat rated throught the temperature ranges considered actually true? For example I've got a chart here for a P&W JT4 which is flat rated to 60 degF, after which thrust falls. Perhaps modern turbofans have a wider range.