To achieve the same CAS on a hot day as opposed to a cold day, you will have a greater ground speed.
Greater groundspeed equals longer take off run, and a greater distance to achieve the same altitude, which means a reduced angle of climb.
I edited my previous post to remove nonsense which refferred to props and horsepower available. For the same CAS drag must be the same, so thrust required must be the same, excess thrust the same, so rate of climb the same.
