I need to make a heat shield to protect the bumper and other parts from muffler heat.  The current shield on my car is made of thin aluminium.  Can I use aramid alone or together with carbon fiber to make such a piece? 

There is no need to use aramide fibers. Cf won't melt as a fiber, the problem is to use proper resin, such as very high temp resin from EC, but you have to post cure it in an oven. After you prepare your Cf part, one that will expose to heat you could wrap with some alu tape.

~~~Everytime I hear sound of demoulding part I have eargasm~~~

As said, its not a problem with the fibres, be it carbon or aramid, but a function of resin TG. You realistically need to measure what the temperature gets upto then decide what to do from there.

Warren Penalver
Easy Composites / Carbon Mods - Technical Support Assistant