Not knowing your area, I can just give some generic suggestions:
1) Is there a children's museum, science museum or environmental center near you? Often the public library has discount passes and you can check it out for free or very little, then consider an annual membership. For one fee, you can go for free all year long including with parents, grandparents, etc. Many other museums have reciprocal memberships, so if you join one, you can visit others. Usually you get a discount on parking fees and even the gift shop - at least that's how it works up in New England.
2) Nature areas? Contact Audubon or other organizations - usually the sanctuaries are free for an annual contribution, and even if it's hot out, many paths are shaded. Sometimes they have an indoor (and in your area, air conditioned) main building with programs, lectures (for kids), demonstrations. Then you can go outside and apply what he has learned.
3) Bike trail? In our area, there are paved-over rail trails that offer safe bike riding (no traffic except other bikes), and if you get out early before the heat hits, you can be done and ready to cool down and still get activity out in the fresh air.
4) Indoor sports arena? We have some in this area with basketball courts and soccer fields - you may have to sign him up for a league, which might not be what you're looking for, but maybe some have open drop-in hours for a membership fee. Again, if you divide the annual fee by the number of visits, it's not as much.
5) Bowling? In New England we have regular ten-pins as well as candlepins. The latter are easier for kids because they use small balls and small pins, the former are often at alleys where (for kids) they put bumpers in the gutters so the big ball at least has a chance of getting down the alley! If you don't buy snacks, it's affordable. They may let kids bowl in their socks, but you may be able to find bowling shoes through something like Freecycle - that lets you save rental fees.
Good luck!