Someone who's bad-tempered is cranky and surly. Your bad-tempered next door neighbor might spend the weekend yelling at kids, "Stay off of my lawn!"
Oscar the Grouch is a good example of a bad-tempered Sesame Street character. Bad-tempered people are grouchy by nature, although you can have a bad-tempered day or an unusually bad-tempered reaction to some terrible news or a visit from your least favorite cousin. Your temper is your state of mind or your mood, so to be bad-tempered is to be in a bad mood.