If you refer to someone's temper or say that they have a temper, you mean that they become angry very easily.

Your temper is the way you are feeling at a particular time. If you are in a good temper, you feel cheerful. If you are in a bad temper, you feel angry and impatient.

To temper something means to make it less extreme.

If someone is in a temper or gets into a temper, the way that they are behaving shows that they are feeling angry and impatient.

If you lose your temper, you become so angry that you shout at someone or show in some other way that you are no longer in control of yourself.