I'd suggest that 74F is not cold, and that no way should he be shivering if living with this indoor temperature. Does your heating stay on overnight, and at that level? Could there have been power outage overnight? Does he have warm bedding to snuggle into? If so, then I'd suggest something else may be going on - dogs shiver for other reasons than feeling cold - fear, pain and something neurological being the other reasons.
I'd suggest too that it's not 'dangerous' to leave a coat on, but whereas we can shed a layer when we feel too hot, dogs cannot so coating him when you can't supervise him (sleeping) isn't a good idea really.
Again I can't see an ambient temperature of around 74 being the cause of all this. You might try upping his food through the Winter months, making sure it's a good quality one. Also that his bed is out of drafts because it's often drafts that can lower the dog's temperature making him shiver. Otherwise maybe it's time to get him in for an overal health check.