Even if the excess thrust relationship is unchanged AND the climb rate is unchanged**, the a/c will be at a faster TAS as temp. rises. Faster TAS vs same RoC = shallower angle.
**Of course the RoC will be reduced, making the gradient worse, but for the sake of argument...
Hawk, I get the impression you're trying to use a Thrust &/or Power &/or Drag graph for a particular circumstance (WAT) and possibly with unsuitable axis (IAS/CAS?) then applying it in slightly different conditions eg different TAS? Just a thought...