I just got back from my mountain flying trip; 5 days to Colorado and back. Lots to say about the trip. One thing I learned first hand was how different it is flying a plane on a 100° day at 9000 feet. It's a little alarming when the plane keeps lumbering down the runway and never wants to take off. Heck, at Telluride we took advantage of the fact the airport is up on a plateau; as soon as you clear the fence you can drop down 1000' into the canyon.
The key idea is density altitude, a measure of air thickness. Little piston airplanes don't fly well in thin air. We need air molecules under the wings to generate lift, oxygen to burn fuel, and airflow to cool the engine. For takeoffs and landings the thicker the air the better: a Cessna 182 needs only 645' of runway to get airborne at sea level but at the highest airport in the US it needs 1430'. Field elevation is the most important thing driving density altitude, but pressure, temperature, and humidity also matter.
At sea level when it's 15°C and 29.92inHg density altitude is roughly 0'. On a warm 30°C day it goes to 1800'. When we took off yesterday from the lowest airport in the US it was so damn hot in Death Valley that it was like being at 2600', despite the airport being at -200'. 10°C is roughly 1000' in density altitude. Hot mountain summers require careful attention to plane performance.