> Our system can store the summer excess production for winter thermal demand.

This concept appears immediately flawed. Heat will definitely escape the "dirt pile" at some point between summer and winter.

Some yes. But there's a flaw in your reasoning: It ignores the concept called "rate of change". Because of this concept there will be more energy put into the pile than escapes, leaving some to be extracted and not just "escaping".

Honestly not bad if there's enough earth between the heater element and the air - you'd only lose about 1% per month with a thick dirt wall.