The death of a "dear friend" is the question in this quotation from Emerson. Who is the dear friend, and why has he died?

Emerson writes, "To a man laboring under calamity . . ."

In this, he is referring to someone whose mind is weighed down by real or imagined misfortune, adversity, disaster, or trouble.

Next, he writes, "the heat of his own fire hath sadness in it . . ."

This means that the normal energy a person has, which includes the range of emotions from joy to fear, is dominated by sadness. The heat is the product of the fire (normal energy), but that heat is now full of sadness.

"Then, there is a kind of contempt of the landscape felt by him . . . "

So, the person feels sad but also contemptuous of "the landscape," or his surroundings, society, and environment. He resents others, often resenting their happiness—the world becomes sad, too.

". . . who has just lost by death a dear friend."

The dear friend is the god-given joy of living. He's lost his greatest companion, the ability to experience happiness and life.

To paraphrase: "To a person beset by disaster, her own life is like a light that shines on only shadows and despair. So the whole world is darkened, like it is for someone who has just witnessed the death of her best friend."

It's hard to paraphrase because any paraphrase removes the poetry of it.

Emerson prefaces the quote with "Nature always wears the color of the spirit."  This helps to accentuate the understanding of the quote.  Emerson makes the argument that individuals are bound by their own subjective in the way in which they interact with the external.  Nature is thus a reflection of our own sensibilities.  It is a reflection of us, and our attitudes towards it mirror our own temperaments.  

A paraphrase of Emerson's quote might be that human beings always view nature through the lens of their own experiences. If heat is associated with toil, one's reaction to the natural world is tempered by such a narrative.  In the same way, there is a pain experienced in the world that serves as backdrop to the loss of a dear one.  The natural world is a reflection of our own experiences and sense of identity.  For Emerson, the "unity of both" subjective experience and external reality becomes critical in one's consciousness.  In order for this unification to happen, one has to grasp the acceptance of how the external is reflective of our own subjective experiences.