We always have the top sheet on here. But if you're looking for somewhere to offload yours, try an animal shelter or vet hospital. I know our local ones really appreciate old towels and sheets!
Great idea!!

I use winter flannelette top sheets (to stop the draughts), and cotton summer ones when it's too hot for the quilt. I have way too many cotton flats, so I might see if my vet wants them!