Drieing can create matting in certain washing/drying machines. It's best to spread them out and let it dry by air. The high washing temperatures removes their natural grease-layer which makes them more matting/tangled/felty when tossed about after. Be sure to when still wet comb then in the shape you need before letting them be air-dryed.

Technically just high temp washing is enough health-wise. Animal hairs are low on the scale of spreading deceases etc. in itself. It is mainly for parasites/fungi that might live in it and can be spreadable to humans. And skinflakes that can trigger allergies in people.