The title mashes "sunburn" and "burnout," and that double meaning sets the tone: this is about being scorched, physically and perhaps mentally. The speaker seems to have trusted the sun as a guide, and the first lines suggest that hesitation ruins the whole idea of "directions to the sun." Doubt gets in the way of any clear path.
Then the sun is "looked upon as a sort / of government," a strange comparison. Judging by the image, it's a distant power people obey, rely on, and suffer under. The last lines turn personal and a little comic: the speaker's "poor face" is "miserably swelled," while the fig, a fruit that ripens in heat, gets nothing from this either. The speaker seems to be saying that the sun's authority has benefited neither fruit nor person.
The mood is dry, wry, and a bit rueful. The poem is short and fragmented, so it feels like the speaker's thoughts are as frazzled as their skin.