Geo thermal air conditioning by natural air circulation

I live in the Caribbean and during the hottest evenings the temperature is around 86 degrees. We use conventional air con in the bedroom set at 80 degrees. The air temperature in the ceiling is much higher than ground level. If we created a natural air flow by having an air vent in the ceiling to allow the hot air to escape and we replaced that air via an air grid buried underground, then cooler air would replace the hot air. There would be no need for a fan to assist this and it could circulate 24/7. We would keep all windows closed. Has anyone built such a system? It would need perhaps 200 ft of buried pipe with an air intake from a shaded cool area