Lay the fleece facedown on a covered ironing board. Avoid pressing the nappier side of the fabric, if possible, as this flattens the nap of the fleece.
Wet a cotton tea towel or press cloth until it is barely damp. Lay the damp towel over the fleece.
Heat a steam iron to the medium heat setting. Use the polyester setting on the iron, if available.
Run the iron over the pressing cloth, back and forth, being careful not to let it touch the uncovered parts of the scarf. Press the steam button as necessary while ironing -- expelling moist steam into the press cloth, so it won't dry out as you iron the scarf. Then reposition the pressing cloth, so that it covers another wrinkled area of the scarf.
Repeat Step 4 until you've ironed the entire scarf.