The dry season, roughly November through April, is the most comfortable time to visit. Morelos is warm year-round — Cuautla sits at around 1,300 meters, low enough to stay mild even in winter — but the rainy season (May through October) brings afternoon downpours that can make an afternoon at the balnearios less appealing.
Weekends and Mexican school holidays fill the balnearios to capacity. If you want the thermal springs without the families, come midweek — Tuesday or Wednesday mornings are noticeably quieter. For those interested in the history rather than the pools, the town marks its revolutionary calendar with real feeling: November 20 (Revolution Day) and the days around April 10 — the anniversary of Zapata's assassination in 1919 — see ceremonies at the monument and the museum that are worth timing a visit around if you have flexibility.