Will putting a Pyrex glass coffee pot directly on the burner cause it to crack?!

It is not meant to withstand that kind of temperature, and form of heat (eg, gas flame) just the lambent heat of the hot plate.

Gas flames from a burner will actually make hot spots on the bottom of the item you are heating. The flame is hottest at the tip of the flame. The section directly above this tip gets the most heat causing hot spots and cool spots next to each other. Glass does not expand and contract well especially when you are putting hot spots next to cooler spots. Add to this the fact that you have a cooler yet liquid inside and you have a recipe for disaster. Parts of the glass try to expand more the other parts and CRACK,,, you have broken glass everywhere. Glass coffee pots are use on heaters that expand the heat over a large area. As noted previously, siphon coffee pots are quite often used over an open flame but are always over something like a candle or oil lantern type wick. These put out enough heat to make the coffee but not anywhere near as much as a gas stove.
Yes, people have done it before, I have done it before... I do not recommend to do it as shattered glass and boiling water is not a good combination.

If you are using a vacuum pot system then you should be fine although it is not recommended for gas heat source. I would recommended using a trivet between the pyrex glass and burner for any heat source, a rewound piece of coat hanger will work. Do not place on direct heat without water and do not leave on heat source for longer than the necessary brewing time. For brewing coffee it is important to maintain the temperature between 195-205 farenheit.

http://www.squidoo.com/green-coffee
http://www.howtodothings.com/food-drink/how-to-use-a-vacuum-pot

I had a Pyrex dish in the oven with Scolloped Potatoes bake in it.

I was cooking brocolli on the stove.

I took the Pyrex dish out of the oven and place it on the burner that was left on accidently.

It blew up and shattered in a million pieces and hot potatoes went everywhere-what a mess! I'm lucky that I was not standing closer to it or I would have had hot cheese all over me....

I wouldn't chance it.

Just my opinion.

Be careful!

PYREX is a '''strange''' form of glass that really doesn't like to be in direct contact with a burner. And while not all direct contact will crack it, I strongly recommend that you use the wire spacer.

If you are using the pot on an automatic coffee maker the pyrex pot does not require the spacer.

It will be fine unless you leave it without any water in it on the burner. I have exploded pyrex bowls doing this I assure you. If you have an electric stove, it is indicated that you do use a metal form.