Well, according to the leaflets supplied with every iPod, the iPod is designed to work at a temperature between 32° to 95° F (0° to 35° C), and list as a nonoperating temperature -4° to 113° F (-20° to 45° C). Also, the same source tells you that it can run with an humidity between 5% and 95% noncondensing.
That is, you could carry around an iPod Shuffle in a hot summer day, or while sking if you keep it tucked in a pocket (I'm not entirely sure I will use the wrist strap of my 6g while sking).
But leaving it in a closed car, on the dashboard, in a hot day would mean killing it: the temperature was enough to deform a plastic card of mine, so it's way hotter than the 45°C listed as a "risky" temperature.
Furthermore, as you could feel on the skin, the water droplets in a sauna are prone to condensing.
Thus, your Shuffle I fear would be as likely to overheat as your 1g.