Most natural shaggy rugs require cleaning with cold or lukewarm water. Avoid hot or warm water as that could lead to shrinkage and possibly even damage.
Attempting to clean a rug yourself with a rental machine may also be tricky. Make sure to check which products are suitable for your rug before applying them. Some products may cause brown or white marks. For this reason, it is best to get in touch with a professional company with experience in cleaning shaggy rugs.