When Dylan Thomas was writing, a lot of people thought he was going to start a new Romantic movement. You know, the obsession with feeling, nature, and the individual that ties together poetry by William Wordsworth (check out "Tintern Abbey"), Samuel Taylor Coleridge (take a gander at "The Rime of the Ancient Mariner"), Lord Byron (coming soon… "She Walks in Beauty"), John Keats (consider "Ode on a Grecian Urn"), and others.
Thomas certainly is a passionate poet, and his intense feelings come close to overwhelming the reader in this poem. But he's also a very organized poet. He chooses a poetic form with a lot of complicated rules to follow – the villanelle – and then he shapes his passion to fit this form. The amazing thing about the poem is that this highly structured form doesn't stifle any of the feeling in his message. When you read poetry that has overwhelming emotion but also a complicated paradigm, or structure, then you know you're reading Dylan Thomas. (Well, it's more than likely, anyway.)