none of these fabrics are warm(er)... they don't emit heat.
it's the way these fabrics are woven which may or may not retain body heat.
you need clothes based on their utility and the local weather. polyester jackets feel warm as their strands are woven closer and they are suitable for travel in open/rain (bike, walk etc) . a pashmina-wool sweater will be of no use on a bike but may feel very cosy indoors. and in the same way, a multi-layered cotton jacket is very efficient in retaining heat and comfortable to wear (breathable fabric).
so, if you live on north pole, you may need several layers of woollen and polyester clothing but in kolkata a polyester/cotton jacket lined with fleece will do just fine.