I have tumble-dried all sorts of bedding and clothes, everything except leather, including furs and silk, when there was an infestation.
I just put it on the "hot" setting with the sensor set to "extra dry". If they are already fairly dry I presume it heats them up to temp for a bit, then detects that they are dry and goes to cool-down. Will confess I never thought about it. But I am sure the entire garment will have been heated up right through all seams and padding.
But after tumbling you have to put them in a moth-proof container with a moth killer, as you know there are moths in the house and you have to protect them from new eggs.
Once you have an infestation, getting rid of it is a lot of work, and you can't leave any loopholes for them to re-establish or continue living. Hoovering a lot, especially behind and under furniture, and round the edges where they like to climb under the gap at the skirting board helps, and you can spray the edges too. I think an upright vac is better as it beats and shakes the carpet to dislodge the larvae and eggs.
You have to put your clean clothes in a wardrobe or drawer that you have cleaned and put moth killer in. The little cardboard ones impregnated with Transfluthrin give off a tiny amount of vapour, just enough to treat a drawer or a sealed crate. You need a few of the hangers to protect a wardrobe. I believe the insecticide breaks down in sunlight, water and fresh air, so it will not fill a room. Remember that scents like cedar and lavender do not kill moths, they just make your holey clothes smell nice.
An real infestation will cost you a fortune in spoiled clothes, bedding and carpet, so is a serious matter.
Once you have got rid of the infestation, in my experience you just need to keep an eye out, and to replace the protectors in drawers and wardrobes every few months. Check the loft as there may be old felt or clothes up there. You can get an automatic sprayer (like an air-wick freshener) that squirts insecticide every half-hour or so, and should kills moths and larvae; I have used them in an empty house when I didn't have time to clean the carpets and move all the furniture.