I wouldn't be so sure that anger is a "temporary state on its own". Some people seem to be angry all the time!
I am being [adjective] can be used to mean that you are only displaying a certain behaviour for a limited period of time.
Contrary to @tchrist, that construction does not strike me as odd at all. In fact, it can convey nuances that the present tense simply cannot. Examples:
He's being facetious; don't pay him any attention.
Here, it's implied that his facetious behaviour, however common, will eventually come to an end. Compare that to:
He's facetious; don't pay him any attention.
The present tense here means that facetiousness is in his nature: in other words, he's always facetious.
I know I'm being overly curious here, but could you be more specific?
(meaning: I'm not usually that curious, but I find that what you said requires elaboration). Compare that to:
I know I'm curious, but could you be more specific?
(meaning: excuse me for always being curious, but I'd like to hear more about that.)
I'll concede that "I am being angry" may sound a bit odd in some contexts. However, I find the following perfectly acceptable:
While you were being angry at the kid for breaking the vase, I attempted to glue the pieces back together.
(meaning: while you were telling the kid off, ...)