Fairly ordinary situation in the lounge, with a 6' x 6' double-glazed patio door at one end, installed to give a 6" recess; the curtain rail is screwed into the lintel above the door leaving said gap between curtains and door. The curtains are eyletted, and are made of fairly thin material, partly to ensure than when drawn back they hang in a narrow vertical bunch giving maximum light through the window.
SWMBO and I had the idea of instead of lining said curtains and spoiling the 'drape', of hanging another curtain in the recess, using thin material and a removable sprung curtain rod. The idea was to use the two air-gaps formed to provide better insulation rather than just making the curtains thicker. Off we went to the local haberdashers, and decided on some thin curtain lining - not the 'thermal' or heavy stuff; cost about £15 as SWMBO already had rod, tape, rings, and cotton to hand.
She knocked up the new curtains in an afternoon, ensuring that gaps at the top and bottom were minimal when hung, and there was enough for a slight overlap in the centre.
So, last night I put wireless weather-station sensors outside the patio door, between the new curtains and the door, and the lounge side of the original curtains, and waited for everything to equilibrate.
Final readings in degC were: lounge 23.5, curtain sensor 10.1, outside -0.1.
It is clear from these figures that the temperature drop across the two curtains at 12.4 degC was greater than that across the patio door at 10.2 degC, meaning the insulating effect of the two curtains and two air-gaps was greater than that of the door. Subjectively the lounge felt more even in temperature.
One thing to try is to repeat the experiment without drawing the new curtains, to see what the temperature drops are, but it seems reasonably clear that the investment of the £15 was well worth it, and the idea of using air as the insulating medium was successful.
It should be noted that the central heating system is controlled by a thermostat in the hall, which was on its usual setting. The lounge temperature at 23.5 degC was probably 1 degC above 'normal', as I aim for 22.5 in the evenings, and might represent a gain due to lower heat losses through the patio door.