The best word to fill in the blank is "sultry."
The complete sentence would be: "On the hot, sultry afternoon, all we wanted to do was relax in the pool."
"Sultry" describes a hot and humid weather condition, which fits well with the context of wanting to relax in a pool.
"Petulant" refers to being childishly sulky or bad-tempered, and "visage" refers to a person's face, so neither of those words would be appropriate in this context.