Any of those dyi air conditioners will work in a pinch so long as it causes the air temp in the room to drop and you don't have the fan blowing at or on the cage. As said chins can't sweat, so a fan will only blow warm air around, and if you blow air at the chin it will get sick. The other problem with using those dyi ones with the bucket of ice and a fan is that you are going to be raising the humidity in the room, not only should chins stay in temps below 70-75 F but also they need to be kept in below 50% humidity.
Other ideas for temp fixes, like for a day, is using bottles of frozen water wrapped in fleece (so the chin doesn't get wet and can't chew the bottle) and put them around inside the cage. You will basically need to switch them out every couple hours for solid frozen ones. You can also in addition to the wrapped ice bottles, you can freeze stone tiles to put in the cage for the chin to sit on, but once again those will need to be changed out when they warm up, so every half hour to an hour maybe. Nothing other then an ac is really going to work long term.
Do you have any friends or family that have ac that you can take the chin to until the heat wave is over or until you get an ac? I don't know about down there, but some vets offices have ac and can board animals too.