The speaker feels out of step with the world around them. Everything outside seems to be softening, dissolving in heat, while the speaker grows colder. That mismatch is the heart of the poem, and the title, "Denialist," gives it an edge: the speaker seems to be refusing something, or perhaps is being accused of refusing it. Given the imagery of melting, it's reasonable to hear a hint of climate anxiety, though the poem never says so directly.
Noon is described as "cruel," as harsh as the "most troublesome god," so the sun feels like a judging, unpredictable power. Against that, the speaker's whole sense of life shrinks to something small and ordinary: a cold drink held in the hands. It's a funny, bleak image. The mood is quiet, numb, and a little ironic, as if the speaker is clinging to a tiny comfort while something huge slips away.