The absolute advantage of thermal underwear is not whether it keeps you warm, but the way in which it wicks perspiration away from your skin, keeping you dry and comfortable.
Cotton absorbs moisture and stays damp - itll chafe you. Tops/pants/long johns made from synthetic fibres like polypropylene or polyester do not absorb moisture but pull it away and transmit to the next layer. Even football shirts do this. The idea is not to have thick thermal underwear but a very thin layer.
If you wear cotton next to the skin in a chilly mountain environment and get hot and sweaty, the casing of water can be the first step to hypothermia.
I like the
Patagonia Capilene range for this, or the
Berghaus base layer range. You can even get sports underwear from M&S which does the same thing.
The layering principle already mentioned is the other important thing.