Good thread.
Recently I was flight testing a Murphy aircraft with a Van's style air box / filter. The air filter is in a plenum, when carb heat is applied the intake to the plenum is blocked and the heated air intake opens. This means that if the filter ices up, there is no alternate air intake, the only option is to melt the ice. Checking the certification requirements that might be applicable to a similarly equipped certified aircraft it requires the carb heat to be able of generating a 100°F rise. I've never seen a system that can deliver this much heat but we have a carb t° probe on the way and we'll see what it can do.
If you are flying an amateur built aircraft, best check how the carb heat / alternate air works.