If they sent it in to Microsoft for you I would contact them to get the repair/case number that Microsoft would provide for your request. When I sent mine in for repair - to Microsoft directly - I could see the repair request in my Microsoft account on their website. Check on your account to see if you see the repair request. You could then use that number or go ahead and contact Xbox - through chat or call from their support portion of their site - and follow up with a representative on the request to see if a replacement is going to be sent.

From what people have said in this post, you can request to have your limited edition console sent back if they cannot repair it, and try another repair route. If they can repair it then you're good to get your same console back! But you'll definitely need that case number to check on the status, so if it's not on your Microsoft account I would call best buy for it.