Perhaps I shoudn't be posting this, as my knowledge is probably vastly inferior to others on this forum. However ....
When I look at the chart posted by MfS, starting at 15C & SL we can derive the T/O distance at the bottom. If we stay at the same temp but move up 2000ft (right) there is an increase to the T/O distance.
Now, start at that T/O distance and look upwards until we reach S/L and find the temperature (about 38deg C).
So for the same T/O distance we have
15degC 2000ft above SL or
39degC at SL
The 2000ft change would represent notionally a 4degC temperature change, much less than the 23 degree change at SL.
From that, I would conclude that the drop in pressure with a small change in height had the same effect as the large rise in temperature (23 degrees).
Thus height has more effect than temp?
Am I wrong?
GB