Baking Dark Chocolate in Cookies Without Burning Them
Dark chocolate is actually more heat resistant than other kinds. Milk chocolate can scorch at 115° F / 46° C or higher; semi-sweet can have problems at 125° F / 52° C or so. It's mainly the dark chocolate that can withstand temperatures as high as 140° F / 60° C.

I think there are two misconceptions to clear up here, those being:


Baking at 350° F does not mean you are raising the internal temperature to anywhere even close to 350° F. Even yeast breads are not baked to an internal temperature higher than around 200° F, and it's much lower for soft breads and especially cookies. It's hard to find much data on the recommended internal temperature for cookies, but I'd estimate it to be around 160° F simply for food safety reasons.
Just because a food can burn above a certain temperature, does not mean that it will happen immediately. Just as heating oil slightly above its smoke point does not immediately result in flames and rancid taste, heating chocolate above the aforementioned temperatures will not immediately cause it to scorch. What it means is that chocolate can be sustained in a melted state indefinitely at lower temperatures, but raising the temperature further will cause it to eventually scorch. The higher the temperature, the less time it will take.


These "scorching" temperatures are mainly cautions against direct stovetop or microwave heating; with these methods it is easy to get the temperature very high, very fast. When you bake cookies, you are applying very slow, gradual heat; if the temperature of the chips even gets as high as 140° F, it won't stay that high for very long. It's not enough to burn, and that is why even milk chocolate or white chocolate chips tend to do fine in cookies.

So just bake them, and don't worry. The cookies themselves will probably scorch before the chocolate does.

P.S. As SAJ14SAJ writes in the comments, this assumes that you bake the cookies on some kind of insulating material like parchment or a baking mat. There is a risk of burning if you bake them directly on a metal tray and the chocolate comes into direct contact with it, as it will then heat up very quickly to approximately the same temperature as the tray. So don't do that - if you use a metal tray or cookie sheet, make sure there's something between that and your cookies. They bake from the ambient heat in the oven, and don't really need direct heat from the tray.