Word or short phrase to describe an individual who does not tend towards extremes of emotions?

I'm not quite sure whether these will be of any help to you but here is my list:

composed

unmoved

equable

even-tempered

imperturbable

stolid

phlegmatic

You may say that the person is a man of equanimity

Definition: Equanimity is a state of psychological stability and composure. It refers to refers to emotional calmness and balance in times of stress.

Example: Having a tranquil mind, the man of equanimity sits in a calm, still posture. He walks with full confidence, without any fear or uncertainty.

Rarer: "a man of sang-froid".

We say a person "is very grounded" and mean by this that the person is emotionally balanced with a sensible disposition.