In "Heart! We Will Forget Him" how would you paraphrase what she means by warmth and light?

I had to edit your question down to
one.

The speaker is trying to forget someone. For whatever
reason, the memory of this person is causing the speaker distress. Perhaps this person
hurt her emotionally or the speaker just misses this
person.

The speaker asks her heart to forget the warmth.
The warmth is the emotional connection to this person. If the heart “forgets” this
overwhelming feeling, it will be easier for the speaker to put this person out of her
mind. The light could refer to the person’s physical appearance which can only be seen
in the light. The light could also refer to the mental connection. The memory exists as
long as there is light to shine upon it. The memory will fade as the light (on the
memory) dims.

Dickinson is using personification by giving
the heart human attributes when she asks the heart to consciously forget. When the
emotional connections (warmth) fades away, the heart will essentially, but not
literally, forget the feeling. This will make it easier for the light that shines on
that memory to “dim.”