Just to comment on these, eat CCs. CCs regen a lot for Pyro. You should beg your opponent to CC you, unless you are being focused, or mid burst with CDs up. Don't blow your heat unless you are near death, can secure a kill / out of combat, or have vent heat up.
CC for Pyro is both offensive and defensive. A well timed stun can be the difference between a solo/group ranked match. Many times I've Thermal'd someone, and stunned them just as it was about to go off, and nuked them. Carbo, on the other hand, is very defensive, allowing you to retreat, or push a single target while controlling the rest.
AP against full tank is a must. The sustainability and aoe/internal pressure allows it to wear down tanks better than any class, no question. Pyro, while burst, is easy to counter, and can lead to overheating against tanks, due to prolonged matches. AP against hybrids isn't great, since hybrids offer more burst, making the match more of a race than a wear-down match, making AP a poor choice.