Yes, and no. Reducing engine bay temperatures was a side effect to what powertuners wanted to achieve in the first place, the primary reason for heat wrapping manifolds and exhaust, was to reduce back pressure from the exhaust system for increase in power.
I'm not an expert on motor engineering, but from what I know of warm air intake, the purpose is to decrease the resistance of air when flowing through the throttle, only making it suitable for (non-turbo?) petrol engines.
For turbo diesels, a manifold and exhaust wrap would (theoretically) increase the energy transferred to the turbo, increase scavenging, lead to higher torque figures and improve fuel economy, however i have not been able to find any dyno test that confirm (nor any that refute) this claim, apart from one done by a manufacturer (of wrap)..
As for fatigue and wear on the wrapped parts, I'm pretty convinced that it's true, but a thing to consider is that most people who wrap their manifolds do it for power increase and drive their cars hard, and usually drive petrol engines, and the temperature of exhaust gas of diesel engines is lower than the exhaust gas of petrol engines. How big a difference that makes is impossible to know, but manifold fatigue is definitely a risk to consider.
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