I'm now sure if it's ok to bake a carbon frame?
The powder paint is baked at 200°C. At this temperature the epoxy holding the carbon together will start to soften. Epoxy has no melting point..it just gradually softens till becoming goo at about 400-600°C depending on epoxy type and quality. I you really want to bake it you should fix the frame in place so it does not warp and hope they used a good quality resin.
The carbon itself is pretty heat resistant.
Carbon fiber composites can be powder coated as long as the resin (epoxy) has a Tg greater than 220°C (with the exception of special ultra-low curing powders that will cure at lower temps). The problem with powder coating carbon fiber without the aid of a conductive base coating is ANY surface defect (minor scratch, area of irregular distribution of fiber to resin, knit line etc.) will be amplified post cure. So it requires very good surface pre-treatment. And because of this is very expensive.