Let us remember that the speaker of this poem is telling his wife not to mourn him when he dies, as the title suggests. The first two stanzas of this unforgettable poem therefore urge the wife to behave with quiet dignity when they part, just as virtuous people die without drama or display. You need to be aware that the first stanza is a simile which offers the comparison of people parting with dignity to show the wife how she and the speaker of the poem should part:

As virtuous men pass mildly away,
And whisper to their souls, to go,
Whilst some of their sad friends do say,
The breath goes now, and some say no:

Like this, therefore, the speaker encourages his wife to say goodbye to him. The image of "melting" in the poem is thus used as a metaphor to reinforce this image - rather than spontaneously and quickly burn, they are to express their feelings and love for each other slowly and with respect, just as candles melt slowly and gradually - not with "tear-floods, nor sigh-tempests move", because, as the speaker says in the second stanza, to react in this undignified manner would actually spoil the sacredness of their love. Displaying their feelings so openly would show a lack of reverence of the special relationship that they had.