The Alentejo gets hot. Summer (July-August) sees temperatures regularly above 35°C and sometimes above 40°C, which makes walking the walled town uncomfortable in the middle of the day. If you visit in summer, go out early morning and late afternoon, and rest in the shade during midday.
The best seasons are spring (March-May) and autumn (September-October), when temperatures are mild (typically 20-28°C), the light is excellent, and the crowds are manageable. Spring in the Alentejo is spectacularly beautiful — the cork oaks are leafing, the wildflowers are out, and the Cromeleque dos Almendres glows in the morning light.
Winter (November-February) is quiet and cool (8-15°C), with occasional rain. Évora's walled town is not unpleasant in winter, and hotels are cheaper. The city has a university so there's always some life, even in the off-season.
The Évora Fair in late June is a large regional market and festival; the city fills up and accommodation is scarce. Book well ahead if visiting then.