How would one go about giving a scientific explanation for artificial skin gradually adapting to certain environments? For example, suppose character C has the ability to adapt to changes in temperature. If C could resist a temperature of 100 °C, but was exposed to 150 °C and adapted to this, what would be at least a plausible explanation?
Electric sensitive alloy crystallisation
This is not very hard sci fi but it's a start The basic idea is that you have an alloy that crystallizes differently depending on electromagnetic fields. The system then could judge the environment and as exposed adjust the crystallisation to find the best results for the given moment. So perhaps in minutes it could find the em field that makes temperature resistance rise at a cost of caustic resistance
Here is a paper outlining the basic idea propably completely in the wrong scope http://iopscience.iop.org/article/10.1088/0022-3727/38/5/010/meta
By having a layer of gases or bubble of gases in the skin!
Explanation: Gases have the hability to transfer heat (like all materials). The transfer work by conduction and convection. Conduction is a transfer wich work essentially in solids and is pretty slow (because heat is transfer from an atom to an other). In fluids, the heat is transfer by convection too. Convection transfer is a transfer by matter mouvement (an easy example to observe, the mouvement of water when it boils).
An other aspect of fluids is viscosity. Viscosity is the "thickness" of a fluid, better explanation than mine. What is important here is that the viscosity change with the temperature. In the case of a gas, it augments. It means the gas move slower when the temperature increase. See the idea?
If the temperature augment, it become harder to move the gas, so it transfer heat with less efficiency.Now you need to find a gas with low conductivty and high viscosity!
Some issues: This solution isn't perfect. The major issue is pressure. When temperature goes up, the pressure to. Too much pressure ? Explosion, but C could have some emergency release system like a sphincter (he would litteraly fart when this is too hot!). Another issue is chemical degradation due to high temperature. I think a gas with the properties I list will be complex and may have some stability issues (even worse, it could be flammable !).
Other solution: There could be way skin degrade with high temperature to reduce the thermal conductivity. But this is no my field and maybe a biologist or a chemist could make an answer in this way.
The skin is something that is constantly renewed and replaced. In animal tissue, epithelial cells replicate and then dry out, to form the wearing surface, and various other cells form the inner layers with various structures to give it its properties. The cells are all copies of the master, with no ability to change.
The cyborg has nonobots that produce the skin. It has a variety of programs in storage and can receive updates. For the elastic matrix, it may have a choice of several materials. Likewise for the wearing surface.
Just like you use different oil in your car depending on climate, these materials have tradeoffs. Good for high temperature may be too stiff or brittle at low. Wider temp range is poorer wearing. So, the nanites can shift production as conditions change, using the most suitable plan. With multiple materials involved and the ability to download updates, a lot of variety is possible.
This is normal biology. Skin adapts all the time.
Organisms adapt to changing circumstances by upregulating or downregulating gene transcription. If I am drinking a lot, my liver adapts by upregulating transcription of metabolic enzymes for alcohol. If I get my ass kicked, genes regulating transcription of testosterone cause it to decrease and my behavior adapts to the circumstances: I am less inclined to fight. Also my mane falls out if I am a male lion. As another example Heat shock proteins are in all eukaryotic cells and are expressed in response to heat or other stressors, The proteins set off a cascade of other cellular actions which help the cell withstand the stress.
Other stressors such as infection or radiation damage have their own induced protective responses, all turning on altered DNA transcription and change in production of various proteins. For example my skin increases production of melanin in response to increased UV damage. My skin increases cellular division in response to friction, and I develop callus. A horse that spends time outside in the cold grows a fur coat. Then when things get warm, it sheds.
It is no great stretch at all for a cell to detect the environment and trigger an adaptive response. Your skin could have adipocytes which accumulate lipid to improve insulation, stimulate growth of adjacent hair follicles or whatever it needs to cope with circumstances. It does not happen within minutes but can happen within days.
The question mandates artificial skin. Make your artificial skin out of cells. They are good at adapting.