How can I prevent tea stored in a thermos from oversteeping?
As posted in comments by members of the community (and adding my own), several tips can help you get good warm tea in your thermos at wake-up:


Choose loose leaves instead of tea bags to avoid tea dust that would overinfuse your tea in the thermos. The small amount there is in tea bags, is heavy enough to sink to the bottom very quickly, so if you pour the tea slowly into your thermos, you can discard it. You can also rinse the tea before brewing with cold water to help expel any excess dust, or (as done in many tea-drinking countries) throw out the first cup of tea made with new tea leaves.
If you're just using tea bags, why not just keep the thermos bedside and then toss the tea bag in in the morning? 
You could try heating cold-infused and strained tea in the evening and put it into the thermos; it has a brewing time of 8 to 12 hours, so you'd have to start this around noon. If you have a microwave close enough to your bed, you could also use cold infusion to make your tea during the night and then give it a blast in the microwave in the morning.