Bro, please stop. I already laughed enough. Sigh, usually I don't ask for sources but.. Where are your sources? Where do you get these ideas? The reason why I know this is totally a lie and not true is because about a week ago, there was an article here on Windows Central, talking about all things battery. And nowhere in that articles states about cases causing battery issues.
Also, about the PC example. Again, seriously? Mobile devices have special made CPU's that are quite different than the one from a PC. A PC's CPU is much more powerful and produces a lot of more heat to where it NEEDS a fan. The mobile devices one are made to not make too much heat. This is an area where many companies are working on getting better. On reducing the heat. Mobile devices (even some laptops) needs to be small and thin (at least phones and tablets). So manufacturers ditch the fan to save space but, they need to fix and prevent any possible overheating that might cause malfunction of the device or even put the customer in danger.
Your theory is interesting but base only on your what? You done testing? Proof? Sources?
I have not tested the icon/930 myself for temps (don't have proper equip) but lets look at what is known.
1. There are a ton of posts about the icon/930 being uncomfortably hot under load in this forum.
2. The area complained about most is the lower right corner.
3. The lower right corner is where the snapdragon 800 CPU is located:
http://www.smartphonefrance.info/Technique/NokiaLumia930/disassembly/disassembly.html - The chip is obviously generating a lot of heat, which is transferred to the phone chassis similar to a heat sink on a CPU.
4. The Snapdragon 800 CPU is programmed to throttle (slow down) when it gets hot. The hotter it gets, the more and longer it throttles.
5. Lithium batteries also have reduced life when very hot.
6. Placing a thick protective case like and otterbox or incipio dualpro on the phone will trap heat that would normally be released into the air around the phone, and hence will slow heat dissipation.
7. Thus, because of the very nature of how components react to heat, performance should be reduced with a case especially when doing tasks that generate heat such as games, apps and charging. How much it is reduced involves numerous variables.
While I doubt a case will be an issue for low powered phones, snapdragon 800 and other high powered chips generate a lot of heat. Thus the impact a case makes will depend on the phone CPU and case itself. The phones will not stop working, but performance will be reduced due to increased throttling in response to heat trapped around the phone. Battery life will also be impacted as heat reduces battery life.