The deepest hole drilled in the earth is the Kora Borehole. At 15,000 meters (49,000 ft), the temperature was projected to reach 570 degrees F (299°C), so drilling was abandoned.
My question is, if you were standing somewhere near the surface of the hole (the Kora hole specifically, or some similar hypothetical hole, it doesn't matter), perhaps at the opening on the surface or if you were somehow magically suspended in the air about 1 mile (1.6 km) into the hole, would you feel hot air rising out of the hole, still warm after its 12 miles (19 km) travel upwards, or would the air have long since cooled beyond noticing? How long would it take for that very hot air to cool as it travels upwards?
EDIT: "This would have to be numerically simulated because it depends greatly on the roughness of the walls, hole diameter, soil composition, temperature gradient, and humidity"
I'm afraid I don't know enough about geology to give any sort of substantial information on some of these points. I can say that the Kora borehole was 9 inches (23 cm) in diameter, and I imagine the walls were fairly rough? The KTB borehole in Bavaria only got to 30,000 feet (9.2 km) before temperatures reached 500 degrees F (260°C) if that helps.