Flow simulation should be your tool.
What didn't work with the model of a heat source inside of a balloon? Why would you define a velocity input?
If you conducted an external study with gravity set on you should be able to see the surrounding air move relative to the balloon and calculate some kind of thrust/velocity.
Thank you, Jon!
I think my biggest issue was that I wasn't sure how to approach this problem. It makes sense now!
Your question is a little odd. In this case, there is no thrust of any kind. What we're looking at is a buoyancy problem. Buoyancy is as simple as the difference in weight of the object (balloon) minus the weight of the displaced fluid (air).
The heat source will expand the balloon. This does not make the balloon lighter, but increases volume and thus the amount of displaced air.