Awkward isn't it, being in 'that time of your life'
I keep our bedroom fairly chilly too, and I'm always throwing my half of the duvet onto Andy - for which he's grateful!
All the rest of the time, he's huddling right under, with a throw over him too....
Harry's in a crate in our room, too - but he's a strange (big!) boy, and tends to lay on the 'chillier' side of his crate, ignoring his lovely fluffy bed and blankets - so we, too, cover his crate with a blanket and a thick fleece throw.
I wonder, as he's smaller and possibly being affected by the cold, whether it might be worth putting his crate outside your bedroom door - leaving the door open a little so he can still see you? It might be more 'sheltered' and warmer for him?
If you're worried about his sneezes and coughs, I too would take him to your vet. In the meantime, it might be worth melting a little honey in warm water for him to drink...that always seem to soothe any ailments Harry might have
I hope he feels better very soon! Sally + Harry x