Satement 1
"higher temp means higher density thus less airframe drag and longer range".
No, this is not true.
Increasing density will not decrease drag.
The higher temperature causes a decrease in density. This reduces power and thrust output at any given RPM, so you must increase RPM.
Increasing RPM increases fuel flow.
If you were initially in ideal conditions for maximum range, then the increased RPM would increase SFC.
This would increase fuel consumption rate and decrease specific range and range.
Although your TAS at any given CAS would have increased, this benefit would be outweighed by the increased SFC.
Statement 2
"higher temp means more thrust required thus more FF thus shorter range."
No, this is not true either.
But as described above, the increased temperature will increase the SFC.
The increased SFC means that each unit of thrust cost more in terms of fuel consumption rate. So to maintain the same thrust you are bruning the fuel faster.
It is this which causes the range to decrease.