I had the same issue and my problem was related to sucking oil into to the air intake and oil deposits on the tip of the sensor in the intake. This happened virtually every time the bike was ran hard and I would come down to an idle.
The bike would idle way down and eventually come back up (a minute or so).
I too thought it was a sensor but it never threw a code. That is the only way I know how to check a sensor, if it throws a code.
There are a lot of threads on this topic and if you do a search you will get a lot of reading.
It is the engine over heat management kicking in. With out some type of EFI fuel management system you wont beat it. I think I remember that on the 06's it was worse than the 05"s. I know it happened to me even with a fuel management system but then I bumped my rpms and fuel up in the Engine Temperature tables and it fixed it.
I had a pretty long high speed run and came off a exit ramp to a stop and it felt like the bike was going to die, shaking and sputtering, had to keep feathering the throttle to keep the rpms up, once I got moving at 30 mph or so life was good again. Scared the piss out of me though. That is when I learned about heat management systems on these bikes.
You didn’t mention what year model, but the 1999 88” model (Magneti-Marelli EFI system) throttle position sensor adjustment is well outlined and best followed as per the service manual. I’m sure the same is documented for later model HD service manuals as well. Note that the procedure requires an accurate milli-volt to volt-range range voltmeter and recommended ECU breakout box interface. I believe there is also mention of an ohm meter check for the temperature sensor. However, if there was anything seriously out of order with either of these sensors that you’d probably be seeing frequent service code warnings. If you were to attempt altering the original throttle position sensor setting you’ll likely affect the A/F control settings in the low throttle positions, perhaps favorably or unfavorably. The idle on many EFI HD’s tends to drift a hundred RPM or more in various temperature, humidity and altitude environments. Yours just might need a simple idle set screw adjustment to ensure worst case hot engine idle is no less than 950RPM.