As a general rule of thumb, any temperature in which you feel comfortable wearing a teeshirt and jeans or shorts is fine for a parrot. If you feel the need to pull on a sweater, it is officially too cold for your bird: they can't put on more feathers like a dog grows a winter coat. They only have the one outfit >.< As for the heat, remember that these are desert parrots, and as long as there isn't a heat advisory telling you that it is unsafe and there is shade, they can be out of doors on hot days.
This is quite a wide spectrum, as I am sure you know. In general, you want to avoid rapid change more than you need to worry about overall temperatures. If there is a sudden cold snap in summer or a heat wave in winter, you need to maintain the temperature in your home within a few degrees. When you are setting about making the change from the summer 80s to the winter 60s, you should not reduce the thermostat more than a few degrees every other day or so. Bird systems are rather delicate, and it is actually a change in temperature that is more likely to make them sick than being too cold or too hot.