I think the conductive heat loss is proportional to the DIFFERENCE between the inside and outside temperatures. In other words, if it's the same temperature inside and outside, then no matter what that temperature is, no heat flows through the walls of the house in either direction.
You said it's 20° outside, and you turn the thermostat down from 70° to 60°. So you'd be reducing the DIFFERENCE between the inside and outside temperatures from 50° to 40°.
From 50 to 40 is a decrease of (10/50) = 20%. So your heat loss ... and the amount that gets added to your heating bill ... becomes 20% less for each hour that the inside and outside temperatures stay like this.
Http://www.nature.com/scitable/topicpage/inheritance-of-traits-by-offspring-follows-predictable-6524... this should answer all questions you have on this specific subject in science
b. Yes, the shape of the sheet will affect the Flux through it. This is because flux is dependent on area of the surface and the area is dependent on the shape of the surface.
