Mérida is hot. Extremadura is the hottest region of mainland Spain in summer, and Mérida in July and August routinely passes 40°C. Even so, July and August are when the city is at its most alive, because the Festival Internacional de Teatro Clásico runs in the Teatro Romano: nightly performances of Greek and Roman drama on the original stage, in the long blue dusk after the worst of the heat has gone. Tickets and rooms book out weeks in advance.
Outside the festival, the best months are April, May, October, and the first half of November. Spring brings wildflowers across the dehesa landscape; autumn is quieter and the river light is excellent. Winter is mild and almost empty of tourists, though the days are short and a few of the smaller sites close earlier.
Avoid late July through mid-August unless you are coming for the festival and can plan around the heat. Easter brings the regional Semana Santa processions; quieter than in Andalucía but worth seeing.