To keep all the shots in the group, we need consistent CoF between bullet and bore. As temperature fluctuates, so do the properties of bullet lube which affect that CoF. So, our challenge as lube cooks is to manage friction while the lube is in three different physical states:
Solid plasticized by liquid of lower freeze point, full liquid which willl experience the full range of temperature/viscosity change, and vapor.
The solid/liquid "mush" phase acts as a high-viscosity, deep-drawing lubricant that prevents the bullet metal from abrading or galling as it is forced through the throat and into the form of the rifled bore. I also theorize that this thick phase of lube helps create a good seal (obturates) between both bullet and throat, and between case neck and chamber as the bullet transitions from case neck to bore because lube displaced from the grooves fills voids. In some instances, lube will fill all the space at the end of the chamber and make a sort of bridge that keeps the bullet from flowing into that area before entering the throat. The temperature of the lube on the bullet at the moment of ignition will have some effect on all this.
Further up the bore, the lube is liquified by heat and pressure and acts as a dynamic film lubricant. Since liquid lube temperature is relative to viscosity, viscosity is relative to "friction", friction is relative to bullet time in the barrel and the shape of the pressure curve, and bullet time is relative to point of impact, it's easy to see why temperature of the bullet and barrel affects the way lube will perform during any given shot.
Some lube can be vaporized during the firing event and some remains behind as a liquid slurry mixed with powder/primer residue. Vapor remaining in the bore condenses in time, and with more time the residue solidifies. Depending on time between shots, bore condition can change drastically.
If you can put together a recipe that has the same drag characteristics no matter the state, then you have solved some major issues. The secret seems to lie in blending wax, oil, and other additives to achieve a lubricant that always acts the same between bullet and bore, regardless of temperature. Unlike microcrystalline and paraffin waxes, Beeswax has very high film strength in the liquid state. Ester oils and castor oil (among other things) also have high film strength and low viscocity indeces, so those types of things work well in the high-speed, liquid phase. The oils help plasticize the solid wax for the initial flow. The problem with some of these super-lubricants is they can be too slippery, and beeswax can be too sticky when cold. Microwax can help control oil flow and reinforce beeswax, but also tends to increase friction when cold while decreasing viscosity when it melts, so it has to be balanced out with other ingredients. Paraffin wax is brittle and doesn't absorb/retain oils as well as some other types of wax, but it does make a very slick, hard film when cold. Carnauba wax makes a very hard film when cold, but it almost acts like an adhesive when a bullet rubs across it at high speed.
A lube also needs to transition from soft wax to liquid very quickly, and resist burning. Sometimes metal soaps extend the useful velocity or upper temperature range, but often cause problems in extreme cold. "Extreme bullet lube" is a monster challenge. It's much easier to make a lube that shoots consistently within a 40-50 degree temperature window and 1000 fps velocity window than one that does it all.
A balanced mix of broad-spectrum microwax, beeswax, paraffin, plasticizing oils, and high film-strength lubricating oils all held together with a metal soap works out pretty well for a lot of us for addressing the cold bore issue, heat fade, leading, high velocity, low velocity, and other issues like hot ammo storage conditions and unheated lube-sizers.