Thinner paper wont do the trick. Get some heat resistant foam (most upholstery foam is) and cut it to be about 1" smaller than your transfer sheet.
Leave the 1" margin blank on the transfer.
Place the foam piece underneath the shirt and then lay the transfer on top of the shirt. As the transfer is larger than the foam piece under the shirt the transfer will stick out.
Press as usual. All four edges of the transfer should be off of the foam. This prevents the edges from creasing the shirt.
Hopefully this helps!