When to go
Sana'a can be quite warm in the summer, and winters are generally cool and enjoyable. Summers are also quite dusty and dry, and your clothes can soon turn an annoying shade of beige as you traverse the city. Hot also means you will be more prone to exhaustion, and you might be tempted to try a locally prepared unhygienic drink just out of immense thirst, with grave consequences. In short - it is better to avoid Sana'a in the summer months.
Unfortunately, it seems, the largest annual festival in Sana'a, one that is held especially to welcome tourists to the city, is held during the whole month of June. This offers perfect insight into the life and culture of the residents. If you love a city for its festivals, its people, and their sense of communal fun, then summer months would be the ideal choice for you to visit the city. Otherwise, it is better to visit the city any time during September-February. The hordes of tourists will be dying out, the city will be cleaner, cooler, and more accessible, and you can get to explore more of local life rather than bumping into a foreigner on every other corner.