1. Cut a peice of cloth from the T-Shirt. Try to get it at the seams so that you do not destroy the T-Shirt. Try not to cut too much, else if the thread comes loose, you will have a gaping hole.

2. Burn it

3a. If the cloth turns to ashses and flakes, and/or if you see while greyish stuff at the edges, it should be 100% cotton.
3b. Another tell tale sign, on a piece of cloth, and the edges curl, it should also be 100% cotton.
3c. Cotton usually crumples easily compared to polyester mix

If the cloth melts, the burnt surface is rough touch, and there is a sweet smell. Then its has cotton with polyester mix. Polyester melts when burnt.

While these methods are not 100% accurate. The most accurate method is to send it for a lab test.

So, can you tell which peice of cloth is 100% cotton and which is polyester cotton mix?