The most available source of coolth seems to be ground temperature, which according to the internet deeper than a meter is about 10-16º year round worldwide, maybe up to 25º if it's real hot outside and you're on wet clay.
So, this idea would be to bury a water drum and pump the air through it. The hot air inlet would enter at the base so that the air bubbles up through the water dumping most of its heat and humidity. Cool air is then drawn out of the airspace at the top of the drum and piped into the building.
The pump can be driven by whatever is available, but a wind turbine would be easy enough and keep the whole system non electrical.
The growing space would have insulated walls and skylights with diffusers to bring the light levels down to about 30% of sunlight, which is optimal for most edible plants. Temperature would be regulated by airflow.
According to some quick, probably wrong, calculations on wolfram it looks like water is about 3000 times the thermal sink of air, ie taking 1º C out of 3000 litres of air would raise a litre of water 1º. Therefor a volume of air 2 meters by 3 by 4 would be balanced by 8 litres of water. So a 200 L steel drum would take care of just about anything, depending on the conductivity of the various walls.
This all seems extremely simple, which I guess means it's either already been done or there's something very wrong with the idea.