So...Two different things.
1) The AIT or "Sensor, Air Temperature" (# 26 on the linked parts fiche) is mounted in the intake plumbing or near/in one of the air filters (especially if using the RamAir or K&N setups. This determines the temp of the outside air coming into the system to determine how dense it is and can also be used in place of/ in conjunction with the MAF (Mass airflow sensor) to aid the ECM in determining the amount of air entering the system.
Original Triumph Rocket III, Classic & Roadster Parts. Search Engine Management System parts using manufacturer microfiche assembly diagrams.
www.adeptpowersports.com
2) The Barometric Sensor or "Sensor, Air Pressure, Airbox (#19) usually is used to help determine your outside air pressure (less barometric pressure = thinner air= less oxygen) Think high altitude makes it hard for YOU to breath (and...the same for your engine). This reads your surroundings and helps the ECM account for the thinner air at altitude and the opposite for sea level air. I am not sure I agree with the original statement that it is affected by heat to a great amount though. I have not actually tried it though to see.
Thinking out loud though for a moment....air on colder days IS MORE dense and on hotter days IS LESS dense, but in an unsealed system that heat can't really generate more air pressure............................
Just keep in mind that these are two different sensors and most of us are not necessarily used to seeing both used in an engine so it's easily confused.