These pedals do get warm with use, but they should never get warm without use, or really hot with use. Those are warning signs.
The tightness of the plate is less important than its relationship to the "lip" of the ceramic piece. It should be just below the lip for good graduation of speed. The nut should be tightened down so that the screw can't back off. Dave McCallm even suggests a little nail polish. Loctite is probably preferable if you have it but nail polish will lock the nut in place too.