I want to preface this response by stating that I place more importance on “real world” experience such as reported by Jim, Frank, and others than I do on the theory. That said, I will attempt to provide a high level summary of Jim Ellis' thermal sleep comfort problem.
When your body burns its food fuel, it is only about 25% efficient. The remaining 75% is released as heat. When sleeping, the average male generates at least 75 watts (metric) or 240 BTUs (English) of heat. To feel thermally comfortable you want to lose 240 BTUs of heat and no more or like Jim Ellis, you are going to be cold. To put this 240 BTUs number in perspective, when we are very active we can generate up to 8 times that amount of energy and waste heat. This is why you sleeping bag insulation has to be so much thicker than what you wear when you are hiking. Heat always moves from a hot object to a cold object. Our objective is figure out how to not loose any more than 240 BTUs of heat regardless of the conditions that we are camping in.
Lets look at Jim’s size, his BA Mica sleeping bag, and his BA Insulated Air Core pad in a 40 degree environment as an example.
His body produces at least 240 BTU/hour (English) or 75 watts (metric). Average (BMR) basal metabolism = 1 kcal/min * 60 min/hr = 60kcal/hour * 4 BTU/kcal = 240 BTU/hr.
His bag is a 20 degree BA Mica. US manufactures typically rate their bags using the ISO TR11079 standard. For a 20 degree rated bag, the top loft would have a .75 m2K/V (Metric) and an R value of 4.26 (English). His BA Insulated Air Core pad has .317 m2K/V (Metric) and an R value of 1.8 (English).
His body size results in an area of about 1.7 meters2 (Metric) or 18.29 ft2 (English). The top half of his body is insulated by the sleeping bag and the lower ½ his body is insulated only by the sleeping pad. He is sleeping in 40 degree weather.
Heat Loss in BTU/hour = Area in ft2 * (Tin-tout) / R value
Heat Loss in BTU/hour from the bag =9.15*(95-40)/4.26 = 118.12 BTU
Heat Loss in BTU/hour from the pad =9.15*(95-40)/1.8 = 279.56 BTU
Total heat loss by (convection/conduction/radiation) = 397.69 BTU
Total heat generation =240 BTU ( He will be cold and the cause will be the pad)
Now lets assume he put a high quality 3/8” foam pad (R=1.72) under his BA Insulated Air Core. The heat loss from the pad would now be calculated as
Heat Loss in BTU/hour from the pad =9.15*(95-40)/(1.8+1.72) = 142.95 BTU
Total heat loss by all mechanisms (convection/conduction/radiation) = 261.08 BTU. By adding a light shirt he would now be in comfortable thermal equilibrium with the 240 BTU he is generating and the 240 BTU he is loosing.
If Jim was a young and highly conditioned mountaineer his BMR could be as high as 100 watts (Metric) or 341.21 BTUs (English). By adding a light shirt he would have been comfortable with just the BA Insulated Air Core.
The above simplified BTU calculations incorporate all of the heat loss mechanisms, assuming you are sheltered from the wind. There are three mechanisms for heat loss which I will next discuss because Paul asked but it is not really important to understand why Jim Ellis was cold.
The activity level of the electrons in air becomes more active as they are heated. When the electrons change orbit they generate photons which is known as radiant heat. This type of heat transfer works like light does. If you can’t see light through your insulation, you probably won’t get radiation loss through it. In a sleeping bag that is more than ¾ to 1” thick, all of the radiation is absorbed by the fibers and heats the bag for you. If you don’t have ¾ to 1” of conventional insulation then an air gap and a foil material will reflect this type of heat back to you. This is the situation in which emergency space blankets are designed to address.
Convection is the actual movement of the heated air molecule because of wind or thermal buoyancy. The wind (forced convection) is primarily prevented by your bivy, tent, or tarp. Natural convection is the upward movement of heated air, its cooling, and its subsequent falling to create a current that moves heat. If you trap air in very small areas, then the viscous forces in air prevent the material from circulating. The sleeping bag insulation breaks up the air into tiny little pockets to minimize this circulation.
Conduction is one molecule vibrating with heat and then randomly bumping into an adjacent molecule to transfer its heat energy. Both the sleeping bag and the pad are designed to solve this heat loss. The pad is also designed to provide cushioning as a secondary consideration. Each material, including the air spaces in the insulation, has a known thermal resistance that is measured in a consistent fashion. Organizations such as NIST, and others, publish data bases of these tests for common materials.
It is prudent for a backpacker to provide a total insulation package (bag and pad) that will loose no more that 75 watts (Metric) or 240 BTUs (English) of heat in the worst case environment they will be in. Having the pad provide a margin of insulation is prudent, because any excess heat can be vented by the sleeping bag zipper.