The speaker conveys a couple of intentions in this poem. First, he wishes to turn the "cold mind" of an unnamed woman into thoughts of more passionate feelings. He believes that through his art, he can sing of love in such novel ways that her heart will no longer be cruel toward him. He wants to see her regret the choices that she's made—namely, rejecting him in some way. The speaker seems to take a sort of pleasure in imagining how this will play out, hoping that her eyes will "grow wet" and do so "quite often" as she realizes her "mistake." All of this is stated rather directly in the first two stanzas.
The second intention is a bit more indirect. The author, presumably the poet speaking as himself, wishes to use all of the angst he has suffered from this "cold" woman to further his own eternal glory. In the last stanza, he notes that he doesn't mind the discontent he faces in the present, because it provides the inspiration he needs to create this poem—and thus reach fame. Interestingly, he was right. Here we are, around seven hundred years later, still reading the words of Petrarch. Whoever this cold woman was, she provided the inspiration needed to create a piece of art that has indeed survived the test of time, reaching audiences in worlds Petrarch could not have imagined. This poem reminds me a great deal of the final couplet in Shakespeare's Sonnet 18, where he proclaims that his poetic works have the ability to give eternal life to the man he's addressing in the poem.
In analyzing poetry, it is generally useful to separate the poet and the speaker, as the author can write in a variety of voices, even within a single work. In his Sonnet 131, Petrarch presents a speaker who is concerned that their beloved does not adequately reciprocate their love. The speaker’s message is directly stated but not addressed to the beloved. The speaker offers a series of hypothetical actions that they would extent toward the beloved, and by doing so, increase her love for them. They would even make her cry (“I’d see…her eyes grow wet") and regret that her previous lack of affection had made them suffer.
Furthermore, the speaker is aware of their potential as a poet in that they discuss the future ramifications of the words of love they plan to record. Achieving lasting renown, even beyond death, as a poet would be adequate recompense (or so they claim) for the less-than-adequate love they are receiving from the beloved.
The images that the speaker uses also emphasize this admiration that will come later. The real-life roses that they see will be covered by the snow—that is, killed by the winter. However, like the speaker’s love, the roses will turn into marble and enjoy eternal appreciation: “glory…in my later fame.”
Petrarch's speaker first conveys the message that the woman he loves is cruel and cold to him. If he could, he would force her to sigh with longing for him, and he would fill her with warm desires for him.
He continues this fantasy in the second stanza, in which he envisions her crying and growing more compassionate, to the point she regrets making him suffer the way she has done.
In the third stanza, the speaker conveys that this fantasy is as likely to take place as seeing roses bloom in the snow or ivory turn into marble.
He finishes by saying he would be glad to turn her coldness to regret—in essence, to continue the painful process of being in an unsatisfactory relationship with her—because, after all, he is more focused on his future glory that his current discontent. What he means by future glory is ambiguous: he could be talking about heaven, or he could he mean his future fame as a poet.
Essentially, the speaker wants to communicate his discontent to his beloved by sending her (or having her read) this verse. He would like her to change and become more compassionate and warm towards him. While he thinks this is unlikely to happen, he says directly that this is his wish.
The message in Petrarch's "Sonnet 131" is that love is hard and leaves one discontented but is still considered glorious to pursue. This message is stated in a way that is not particularly direct. The body of the poem, while essential for understanding the ways the poet things that love is cold and that it only takes but does not give, interrupts the sentence that gives the clearest idea of the poem's meaning:
I'd sing of love in such a novel fashion...because I do not mind
my discontentment in this one short life,
but glory rather in my later fame.
Here, Petrarch appears to be making a bit of a joke about his position as a poet. The glory he expects seems to be the glory of a poet well remembered. So, the message of the poem revolves around the idea that people will glorify poets who speak of love in such novel ways, even though love itself is cold, unfeeling, and so often disappointing.
In the first two stanzas, the speaker relates to a "love" that he is unable to woo at first. He must work hard at it, drawing “by force/a thousand sighs a day, kindling again/in her cold mind a thousand high desires.” The second stanza suggests that this person has done him wrong. He’s comparing his love to someone “who feels regret...for causing someone’s suffering by mistake.” While this is a comparison, it still suggests that she’s not treated him fairly, but that he’s willing to look past that.
The scarlet roses in the snow and the ivory that “turns to marble those who see in near them” can be looked at symbolically. There’s a sense of purity, but also of blemish. Again, he’s willing to let the “blemish” of the roses roll past him because of his love for her. Finally, in the last stanza, he knows that this will cause great suffering, but he doesn’t “mind/[his] discontentment in this one short life,/but [looks for] glory rather in [his] later fame. The later fame is the afterlife.