Based on my experiment, baking a Dollar Tree mug at 250 degrees for 2 hours provided the best results. The color of the paint remained largely the same and paint on the mug did not chip at all (except for the minor top chipping).
Easy Crafts To Make and Sell - Dotted Sharpie Mugs - Cool Homemade Craft Projects You Can Sell On Etsy, at Craft Fairs, Online and in Stores. Quick and Cheap DIY Ideas that Adults and Even Teens Can M (Cool Crafts To Sell)
DIY Craft Project: Sharpie Mug Tutorial - Custom heart handle mugs that require no artistic ability or transfers! If you can trace and make dots you can make these mugs! Learn the easy hack! Uses oil based Sharpie paint pens that are baked on.