The links below are to a guy who has pioneered the use of SHCS in (conventional) greenhouses. The basic concept is to bury a bunch of drain pipes below your greenhouse and, using a fan, pump hot air from the highest point in your greenhouse during the day, and store it in the thermal mass of the ground below. Then at night or in winter, the fan is reversed and the heat stored below is used to keep the greenhouse warm. Why not incorporate this into a walipini design? It should be possible to have a year-round, very warm walipini using this method. I'll be building one next year and would like to incorporate these two ideas together. I recently scored 40 insulated sliding glass doors from an apartment rental (total cost $10 in gas!) so I've got about 600' of glazing.
http://www.sunnyjohn.com/indexpages/shcs.htm
http://plaintosea.com/phpBB2/viewforum.php?f=7 
