Decrement Delay
This is a fairly new subject which is about how insulation behaves in a dynamic situation (dynamic in the sense of fluctuating temperatures). It is quite a simple subject in theory but there are immense numbers of variables in terms of materials and their positioning and also with regard to climate. It still does not figure in the building regulations although it can have a very marked effect on how insulation behaves.
Because it is a new and complex subject you will need expert advice if you are thinking about using the building’s fabric in this way.
The traditional way to evaluate insulation in a wall or roof is to assume a steady state where the temperature on one side of the insulation is fixed at one level and on the other side it is fixed at a different level and then see (or predict) how quickly heat flows through the wall. For instance a 225mm thick solid brick wall (which has very little insulation) with a winter air temperature on the outside of 0°c and a temperature on the inside of 20°c will have a certain number of watts per square metre escaping out through the wall (about 53 watts/sq.m.).

Similarly in summer the same wall might be at 40°c with the sun beating down on it and if it is 20°c inside then heat will transfer towards the inside.

It gets more interesting when you have a situation where there is the same summer temperature but you start with a cold wall (cold from the night before) rather than one which is already warm. The heat starts moving in through the wall but before it gets through it has to heat up the bricks, so it gets delayed and only seriously starts to show up on the inside after a good few hours.

Similarly, when it starts cooling down at night it takes considerable time for the hot bricks to cool down so much of their heat goes into the room before it starts to travel to the outside. In this way a time lag has been introduced. It’s a bit like the time lag with the earth’s seasons which causes the coldest months to be around January/February rather than in December and the hottest ones to be July/August rather than June when the sun is highest.

The trick is to design walls and roofs so that there is about a 12 hour time lag so that it is always exactly out of phase with the sun. In this way you can cancel out the effects of overheating and overcooling.
It is important to notice that this only works when there is an outside temperature range which swings above and below the indoor desired temperature. Ideally it swings equal amounts both directions. None of this works in a very long, even, hot or cold spell. Only insulation will work then because once the bricks have heated up (or cooled down) after (say) 12 hours they cannot soak up (or give out) any more heat.
The really interesting bit comes when you have a wall which includes mass and insulation either combined (such as insulating clay blocks) or in sandwich layers using dense materials such as woodfibre board. It gets more complicated if you vary the position and size of layers because you can play around with the decrement factor to create different decrement delays. The diagram below shows heat coming in quickly through the insulation (but much less of it) and then slowing down when it hits the thermal mass of the solid wall.

Later on during the night the trapped heat has trouble getting out through the insulation so it goes into the room.

The obvious application for this is in desert areas where it is regularly very hot during the day and very cold at night but in the UK climate there are also seasonal periods when this effect can be utilized, especially in the spring and autumn months.
There is an interesting study from the Netherlands which shows two identical houses, except one has a high decrement time and the other not. The graph on the right in this study has a blue trace showing the lower swing of internal temperature.
Various suppliers are publishing information on decrement times -
Natural Building Technologies NBT show decrement delays between 2.6 and 9 hours (depending on construction) in their literature for pitched roofs.