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to #1: if you don't have a problem, don't create one. Embouchure and "tongue" changes are for teachers experienced in fixing problems! Tongue position can come into play for extreme high register, fast slurs and "lip trills"
to #2: there is no such thing as exhaling "cool" air. The air you breathe in is warmed up by the body. Air speed alone is inconsequential in brass playing (there will be controversy on this point!).

The basics of creating a tone say that moving air forces the lips to "resonate". In this case it means open and close at a specific frequency - like a switch. The volume or pitch produced are based on lip tissue tension (more compression= higher resonant frequency), aperture size(larger hole= more volume, less pressure) and lastly air PRESSURE(this essentially blows the lips "open").
Velocity is a product of air PRESSURE and everything that inhibits airflow like resistance of the mouthpiece/instrument, aperture size and tongue position. Less resistance=lower velocity. This is why a smaller mouthpiece with a tighter backbore and throat CAN aid high register playing. More resistance=higher pressure=higher velocity.
Pressure is a product of lung capacity, diaphragm condition, quantity of air inhaled and everything that inhibits the air flow. High resistance= high pressure.

This is of course greatly simplified - but you should get my point: the more factors you worry about, the worse your playing gets. If you can slur quickly and can play "lip trills", your tongue is just fine. If you can't - get professional help. The problem could be one or many factors! Just addressing one could make the total picture worse! The deciding factor is what you cannot play - never some theoretical model of how something should work!

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Whenever I feel blue, I start breathing again.