I understand that the official height for temperature measurement is 1.5m above open ground. But, how does height above ground affect temperature? My Tempest is roughly 2.5x the recommended height. What kind of error should I expect?
My recollection is the usual number was something like 4 degF per 1000 feet of elevation, so I wouldn’t expect any differences worth worrying about unless you’re suspending your Tempest from a really high-flying drone 
What’s more important is your surroundings. Are you going to get reflected heat off something or pockets of hot/cold air due to wind bouncing off a solid fence and running upward to the Tempest.
(I saw a lot of evidence of the latter here on my Davis gear when I didn’t have it quite high enough on the pole. When I had strong wind from the north off of the (cold) Puget Sound, I’d see a lot of bounciness in the temperature readings when a cold gust happened from just the right direction.)
Short answer is don’t sweat it. Optimize your installation for whatever is more important to you, wind or temperature. In a single sensor system you can’t optimize for both.
There is no firm answer to that question. There is a standard answer as @vinceskahan pointed out but you will have to determine if that holds true for your location.