What you are doing sounds similar to some ideas I've seen with heating passive greenhouses. The video below is an example, but there are a lot on the internet. They normally just vent hot air from the top of the greenhouse into the soil underneath, which is then released at night and maintains a more constant temperature. The video is a slight diversion from that as they are using an old oil tank burried underneath to store more heat.
https://www.youtube. com/watch?v=LgsniiYCwFQ
(to access the link, delete the space between 'youtube.' and 'com'.