If it's ceramic, you have to be a bit careful. Most bundt pans are aluminum. Most of the rest are silicone. There might be a steel one out there, but it's not the norm.

If the cake is cool enough to turn out, the pan should only be warm. You can cool it the rest of the way with the cool water you use to rinse it, which you really need to do between cakes. Dry it well, and you're set to go.

Or borrow a second bundt pan. :)

If the batter is mixed up and is enough for two cakes at once, you really MUST make and bake immediately due to the type of chemical leavening. Once the leavening ingredients (soda, baking powder) have been activated with the liquid ingredients, they need to be baked immediately for the best results. That's why ovens need to be preheated - you never want any type of recipe that is leavened with chemical leavening waiting for the oven to heat. The leavening is activated twice, once when it's mixed with the liquid, and the second time when it hits the heat from the oven. You won't want half the batter to wait in the bowl while one cake finishes baking or the "umph" from the leavening ingredients will diminish and the cakes will be different sizes.

Secondary point: If it's important for the cakes to be very close to the same size, it would be important to have two identical pans and to weigh the batter in both pans when you fill them to assure they have the same amount of batter in both. This will also help them to bake evenly at the same time in the oven.

Last point: If you can mix the batter for each cake separately, then it wouldn't matter. Just make the first cake and place it to cool on a rack. Wait for the pan to cool, wash and dry thoroughly, and make and bake the second cake.

-Grainlady