If you use one layer of dupioni, it should be quite thin and not warm. Hemp silk will be cooler (and softer) though, because of the hemp. But it's also more expensive.

Here's a good rundown of fabric types and their appropriateness as a sling:
http://www.sleepingbaby.net/jan/Baby/fabric.html
As long as you use appropriately sized rings (I'd recommend grippier Aluminum rings with smoother fabrics like silk) and not make the sling too wide so the fabric is easy to adjust through the rings, it shouldn't be any harder than a regular cotton sling. You can test the width & ring adjustment by using it a no-sew RS first before you start sewing.
Silk dupioni is machine washable, though it will shrink a bit and lose its luster when washed multiple times. Hemp silk should be machine washable no worries. HTH!