Making a T-shirt Quilt Using Polar Fleece?

Why not just cut the front of the t-shirts off and just sew the front to the square of fleece. I have seen pictures of quilts where the squares are tied together, but they have used different materials. My thought is that the t-shirts might be more stretchable than the fleece, and you could end up with something that gets out of shape.

Different t-shirts also have a different amount of stretch. I have seen where people make quilts out of t -shirts but they just use the fronts of the tee shirts cut into squares and sewed together and then proceed like for any quilt.

If this is because your daughter wants to use some of her t-shirts in a quilt for keepsakes, I have used some of my daughters t-shirts and made throw pillows out of them. I cut the front and back parts into the size square that I want and sew them together, leaving one end open in order to either insert a pillow form or to stuff it with fiber fill and then sew the open end up.