I have two suggestions. One is a sleep sack. They carry them at babies R us and most Toys R us stores. Many people think of them only for young babies, but they area actually made up to size 18 months or 24 months. It's basically a blanket in the form of a zippered sack with arm holes and a head hole.
Secondly, we have a fan with a small heating element, it doesn't put out the kind of heat that a space heater does, but I also don't have any fear of it catching fire either. We put it on the floor of her bedroom and turn it on at naptime and bedtime and it works really well for us.
Also, are you using a blanket? At 14 months, my pediatrician did say it was okay to place a (not bulky) blanket over our child while she slept. She actually does a decent job of leaving it on most of the time.
Only other suggestion I have is to find the thickest blanket sleepers you can find and maybe put a longsleeve onsie on under it.
Hope some of this is helpful to you.
R.