No, your line of argument is not correct.
Drag = CD 1/2RhoVsquared S
Where 1/2RhoVsquared is the dynamic pressure.
The ASI gives us the indicated airspeed IAS, by measuring dynamic pressure.
The ASI is simply a pressure gauge that happens to be marked in knots instead of psi.
Every time the ASI measures the same dynamic pressure it will give the same airspeed indication.
This means that if we climb or descend at constant IAS, we are climbing or descending at constant dynamic pressure.
This in turn means that if we keep CD and S constant we will always get the same drag. This is why the drag against IAS curve does not vary with altitude. (Strictly speaking I should say the drag against EAS curve, but IAS and EAS are pretty close at reasonably low altitudes)
So changes in temperature or altitude will not change the drag at any given EAS (and will not change drag very much at any given IAS).
The TAS at any given IAS or EAS depends on air density (we discussed this subject in this forum several months ago). This means that as temperature or altitude increase, the TAS at any given IAS or EAS increases (this is why the ECT lines behave the way they do). But the drag remains constant(ish).
Power required = Drag x TAS.
So as temperature or altitrude increase the drag remains constant while the Power Required increases. (because the TAS in the "Power Required = Drag x TAS" equation is increasing)
So as temperature or altitude increase at any given IAS
Drag remains constant
Power Required increases.
You are correct in saying that decreasing temperature, increases air density and this increases both thrust and power available.
So the overall effect of increasing temperature or increasing altitude at constant IAS is
Drag remains constant(ish)
Thrust Increases
These effects cause excess thrust and angle of climb to decrease.
And
Power Required increases.
Power Available decreases.
These effects cause excess power and rate of climb to decrease.
When the aeroplane reaches its absolute ceiling
Thrust = drag so excess thrust and best angle of climb = zero
Power available = power required, so excess power and best rate of climb = zero.
If temperature or altitude decrease, the effects are reversed, so that best angle of climb and best rate of climb both increase.