General warmth:

* Warmth (most common)

* Heat (more formal)

* Warmness

Warmth from a person:

* Affection

* Kindness

* Tenderness

Warmth from an object:

* Temperature (scientific)

* Heat (general)

* Warmth (more specific)

The best noun to use will depend on the specific situation and the nuance you want to convey.