There are three ways that heat transfers - convection, conduction and radiation
Convection is the heat that rises from a hot object. Think steam from a pot, smoke from a cigarette etc
Conduction is the heat from direct contact... hand on hot iron etc
Radiation is the heat projected in all directions, as heat has similar properties to visible light on the electromagnetic spectrum.
Yes, wrap would slow the rate of heat that comes from the metal manifold. In a contained environment the heat would slowly build up until a temperature equilibrium was reached averaging all contact surfaces of that contained environment.
An engine bay isn't a contained environment though - it has air flow. Think of two scenarios.
1. unwrapped metal exhaust with surface temp of 500 deg. Convection means that 500 deg heat is rising into the engine bay (if no surrounding airflow). 500 deg of heat is conducting to the film of air adjacent to the manifold, 500deg of heat is radiating into all other components, which also convects, conducts and radiates that heat back into the next object... and so on.
2. wrapped exhaust with wrap surface temp of 150deg. Actual metal exhaust temp might be 700deg, but is not exposed.
Convection, conduction and radiation of the specific heat is only 150 deg.
Introduce airflow and most of the convected and conducted heat is blown away. Radiant heat becomes the only heat affecting surrounding engine bay components, and only at 150deg.
I'm not an engineer, so happy to be corrected.