If you're doing it right, your oven will be full of turkey. These desserts are okay with that.
Greek Yogurt Cheesecake With Pomegranate Syrup
Get the recipe at Bon Appétit.
Source: bonappetit.com
Pumpkin Cream Pie With Maple Whipped Cream
Get the recipe at Joy the Baker.
Source: farm5.static.flickr.com
Full disclosure: the gingersnap cookie crust in this pie and a few others below does call for a quick (like, 15-minute) pre-bake in the oven. That should be easy to do ahead of time, BUT if you're really opposed to that idea or for some reason don't actually have an oven (in which case STOP, please do NOT attempt to cook Thanksgiving) you can also just buy a pre-made cookie or graham cracker crust.
Nutella Cheesecake
Source: farm8.staticflickr.com