Climbing on a hot day at certain IAS or CAS, associated TAS will be higher and therefore DRAG. If drag is increased, then Power needed will be increase and so, excess of power will be reduced.( even assuming available thrust remain constant cause of flat rated engine operating below reference temperature).
If excess thrust is reduced, then both rate and angle of climb will be reduced when operating on a hot day.
So it is a fact that aeroplanes climb better on cold days.
REGARDS