When constructing a paraphrase, the writer attempts to put an original text into his or her own words. Unlike a summary, which is typically much shorter than the original text, a paraphrase can be just as long as, if not longer than, the original text. You have asked for a paraphrase of the following statement,

To a man laboring under calamity, the heat of his own fire hath sadness in it.

First, we can broaden the gendered noun man to person, because the statement seems to be meant in a general way rather than something that is truly specific to men only: it applies to people in general. Then we must take apart what it means to labor under calamity. Next, what does Emerson mean when he references man's fire? This seems figurative, surely, since we don't literally contain fire within ourselves. Fire is often symbolic of passion, of very strong feeling, and linking it to emotion feels appropriate here, because the fire is said to have a "sadness in it." Thus, we might paraphrase the sentence as follows:

To a person who is dealing with a tragedy or disaster, the strength of his passion—perhaps to solve or address or assist—is tinged with sadness.

A calamity is:

1. An event that brings terrible loss, lasting distress, or severe affliction; a disaster: A hurricane would be a calamity for this low-lying coastal region.
2. Dire distress resulting from loss or tragedy. (www.dictionary.com)

If I had to paraphrase this epigram, it might read something like this:

Humankind faces many adversities in their lives; these include losses of loved ones, financial difficulties, etc.  Despite having to face these, humankind still has the desire to carry on and power through these difficulties; however, doing so will be with a sense of sadness.

This saying makes me think of the fire fighters, police officers, and other rescue workers who searched the debris of the Twin Towers for survivors. The collapse of those buildings can certainly be called a calamity (really, that's an understatement). The people looking for any sign of life were heated, or extremely eager, to find someone alive. Yet, at the same time they were extremely sad because they knew that many people were dead and that it would be unlikely for them to find survivors.

You might paraphrase this statement as: To someone working under severe circumstances, the desire to finish the job comes with sadness.