From your description, this means that air warfare the way we understand it won't be invented at all. If a single bar of the material the size of a water bottle (let's be generous and say 1L) can lift a ton, then individual "flying packs" would have been possible: a backpack sized unit with a small heating element and reservoir of fuel would be sufficient to lift an individual with plenty of excess. The real issues initially would be how to control the lift (I am going to assume the amount of lift must be proportional to the temperature of the metal). So the unit has a control valve which can be accessed from the flyer's hand to raise and lower the temperature.
Quick, I need a match to start this backpack
Now as described, the metal simply provides lift so people will initially be used more or less as kites, otherwise they will be blown about by the wind, without very much control. A person acting as a kite can observe and signal to the troops below, providing intelligence, correcting artillery fire and possibly being used to throw grenades at enemies below.
Now this may seem rather counter-intuitive, but since this is obviously superior to balloons or ornithopters (the only known or considered means of flight prior to this point) yet entirely unlike either one, people will go for the easiest and most obvious applications at first.
Another way unobtanium will change things is in logistics. Heavily laden carts, artillery and limbers and other wheeled vehicles of the period were slow, hard riding and often churned up roads (or sank in the mud). Attaching an unobtanium lift unit to the cart or other wheeled vehicles allows them to float off the roads. With careful adjustments, they can float at low altitude (like a metre) so a horse team can still draw them without damaging the roadway. Care must be taken in windy conditions, but the fuel supply can be cut and cold water poured on the unobtanium to ground the cart, which then is pulled in the usual fashion until conditions are right for floating again.
So at least initially, unobtanium will not lead to air war or air transport.
As more experience is gained with the use of unobtanium, people may develop special suits to provide warmth and later pressurization to fly higher (and larger backpacks with more fuel). The idea of bombing the enemy may be extended so large carts or even specially designed rafts will be lofted, and crews can throw bombs, darts or even launch rocket projectiles. Guns will be out, since the recoil force will cause the platform to violently recoil. This may eventually be overcome by using the scaling properties of the unobtanium to build full fledged fortresses out of stone or concrete and metal and float them over important features or tow them into position as fire support platforms. Several hundred kilograms and a furnace in the middle of the structure provide lift.
Didn't expect that
In an unintentional irony, the use of these platforms may lead to winged flight, since gliders or ornithopter-like flying machines can be safely raised high enough to be launched. Given the lack of compact and sufficiently powerful engines, gliding flight may all that can be accomplished for a long time. Air superiority will then consist of protecting floating platforms, or having gliders swoop down on columns of transport vehicles floating just off the surface of the roadway, with the pilot madly throwing bombs or releasing darts as he swoops by.
Cayley 1804 glider