In my experience, a Pyrex bowl works well as a double boiler. However, Pyrex bowls are not designed for stove top use so proceed at your own risk.
Despite the name, when using a double boiler the heat should not actually bring the water to a boil. The low heat levels should be safe for your Pyrex especially when you consider they are safe to use inside the oven.
For reference, on my stove I make scrambled eggs and fry pork chops with a heat setting of about 4.5 out of 10. When I am using a Pyrex as a double boiler the heat is about a 5 out of 10.
155 Degrees Fahrenheit
One thing to consider is how big the pot is relative to the bowl. You want plenty of room to grab the Pyrex without getting too close to the pot. I have used a 2.5 quart Pyrex and a pot with a 7 inch inside diameter. A 2.5 quart Pyrex bowl is 10 inches across at the top. With this setup I was able to get the contents of the top of the double boiler up to 155 degrees Fahrenheit. This is hot enough to melt the butter in my pudding recipe.
170 Degrees Fahrenheit
Unfortunately, the setup described above will not get hot enough to make something like custard. Custard recipes that call for a double boiler are taking advantage of the emulsifying abilities of an egg yolk without cooking them.
Using a pot with a 7 inch diameter will not heat the Pyrex enough to bring the contents to 170 degrees Fahrenheit. I ended up using an 8 inch pot, the bottom of my stainless steel steamer, with a 4 quart Pyrex bowl to get to 170 degrees Fahrenheit.
A 2.5 quart Pyrex also fits in an 8 inch pot if that is what you have at home. However, the 4 quart gives you some extra distance between the edge of the glass bowl and the heated pot.
An important thing to keep an eye on is the water level inside the pot. If the water evaporates the pot will heat up like a frying pan does. I think this is where there is a risk of damaging the sides of the Pyrex. You can also ruin the surface of the pot with continued heat and no water.
Chances are you will be watching whatever is in the top of the double boiler quite carefully. It would be a pretty big oversight not to notice the water running out.
If you have any experience using a Pyrex as a double boiler be sure to let us know about it in the comment section below.