Cunning plan....NOT!

I was in someone's house once that had a log burner and they left the doors open to let the heat spread through the house and this did work

The problem with this spec is there is a passageway between the dining room and the living room.The warm air would need to go through the dining room door, along the passage and into the living room door. The warm air would rather travel up the stairs than go along the passage and do a right angled turn!