im going with the assumption that your house is pretty well insulated... in that case you can create some ducks at the top and base of your house and create a convection current of airflow. should help keep your house considerably cooler without the use of AC .... bonus cooling if your have a small water feature near the base ducks , the cool water will help cool the air before it enters your house , resulting in cleaner cooler air flowing in your house!!!

Having a large difference in temperatures between two places would lend itself to building a Stirling engine. This would fulfill your criteria of being both interesting and useful. The movement generated could be used for any number of things from generating electricity (although possibly not very much) to just being a nice moving sculpture in your house.

Make a hole in your roof to let the heat escape. This would be useful to you, and interesting to your neighbours.

You could make use of the 'Seebeck Effect', which I've also heard called the 'Thompson Effect', to generate electricity. The general principle involves joints between different metals at different temperatures. In other words, if you took a piece of steel wire, and a piece of copper wire, and twisted the ends of them together, placing one joint in iced water, and the other in some kind of hot place, a small current, probably in the µA range, would flow. The same could be made to work with the temperature difference in your house, though what you'd get wouldn't be sufficient to power anything, especially given the amount of resistance present in the length of wire you'd need. So don't expect to make significant inroads on your electricity bill!

In New Zealand there is a commercial system called DVS which uses the warm air from the loft and redistributes it around the house. Air is taken from the house (using a small fan) and it is heated via a heat exchanger in the loft and returned to a number of rooms via ducting. Apart from saving energy the manufacturers claim that condensation is reduced.  This web sites holds more info. http://www.dvs.co.nz/index.php/pi_pageid/3