Is it
Coin
?
Hard at heart, I can be shaped the same,
A coin heart is hard, but texture is same, size is same from the heart to the end.
Thickened, I added to Nostradamus's fame, My two faces are sharp or
sweet
A coin has two face, a face of hard/sharp icon and a face of flower [sweet]
While the air grows warm, I am a delightful treat
We roll a coin by the air supported beside, a coin is delightfully rolling.
Often in pairs, but enjoyed alone.
Pop me in your mouth and try not to moan.
A coin is often seems pairs because of its two face. but we can always see one face when we put it on a surface.
You can't moan coin in your mouth.
HINT:
I have a bag of these on the desk in front of me.
We usually put coins in bag and you put it on your desk, isn't it? ^_^