This idiom or expression like phrase means:

Toned down.
Calmed down.

When someone says “Her optimism is tempered by what she knows,” they mean something like “Because of what she knows, her optimism and expectation has been toned down. She knows we cannot be too optimistic or hopeful.”

This idiom or expression represents:

Sign of hope.

When someone says “I see the light at the end of the tunnel,” they mean something like “I am optimistic, or I have a feeling things will be getting better soon.”