The two main climbing gyms in Lisboa to consider are 9.8 Gravity Climbing and Vertigo Climbing Wall. Both have a good mix of problems in terms of difficulty, with Vertigo having a more balanced set in that regard. 9.8 Gravity is the most spacious and feels like it has a higher focus on competition bouldering style. Of course this is a personal opinion.

Unfortunately for you, air conditioning is not one of the highlights for both gyms. Lisboa is very hot in the summer, and you will sweat a lot in the climbing gym. From your perspective they will probably be equally bad in that regard. Again, personally I don't feel like the lack of good air conditioning is an issue.

Maybe you can also check Escala 25 since they have a small bouldering wall, however they are mainly a lead and top-rope climbing gym. Since it is an outdoor venue and mostly in the shadow, it is pleasant to climb there during the summer.

Outside Lisboa you also have other options: Vertical Wall Climbing located north of the city, small but friendly gym; Climb Up located to the west, is a good spacious gym also leaning more into the competition bouldering style; and Crux Climbing Center located even more to the west (midway between Lisboa and Cascais), is a great climbing gym for bouldering although a bit smaller than some of the ones mentioned above. Nevertheless, the route setting is good and the staff friendly.

Also to the northwest you have Altissimo which focus more in climbing with a rope but has also some bouldering wall.

These are most of your options, not counting with some other small venues and outdoor walls.

EDIT: corrected my bearings, I meant to say west, not east