Hot air gun temperature
It's not super critical, but if you can control the temperature, set it to 100ºC - 200ºC, and keep the heatshrink a couple inches away. The heatshrink will shrink quickly, you shouldn't have to worry about the stuff inside melting.

If you have a less sophisticated heatgun that runs at 600ºC, it will still work, but you might want to wave it around a bit and hold it a little further away to reduce the temperature. Basically, as soon as the heatshrink starts to shrink, that's warm enough, and it shouldn't take too long.

If you've not bought one yet (asking for product recommendations is off-topic here, but oh well, it's Christmas), a hot air soldering station might be a good choice. You can find some cheap ones on your online retailer of choice, and they make great controlled-temperature heatguns as well as, ya know, hot air rework tools. Which may come in handy.