The routers I have used in cabinets seem to run much hotter than routers run in open air. I am therefore not a big fan of cabinets. I am performance over appearance. Part of the problem with the cabinets I have used (they weren't mine) may have been that they didn't have adequate draft. If you are using a 4 " vac hose then you should have 2x2x3.14159 square inches of opening around the router for proper air flow. This isn't just for your router, it's also for your vac system. Running it without adequate flow will heat it up too. Maybe other members will have different experiences.
Someone I consider a master woodworker once told me that a master woodworker is not someone who never makes mistakes. He is someone who is able to cover them up so that no one can tell.