I have a character that has powerful psychic abilites, these enable him to, among otherthings fly at high speeds and create transparent forcefields. However since these force fields are transparent, that creates some potential vulnerabilities. When he flies at a high speed this will cause compressive heating in the air in front of him, if he flies fast enough, this will cause the air to get hot enough to start glowing and emitting infrared and visible radiation. That is a potential hazard and a limiting factor to have fast he can fly. So how fast can this safely guy fly, and how can he improve this limit, other then flying higher up.
If you are subsonic, you should be fine. If you are supersonic what you can calculate is the stagnation temperature and if you are going at about 3 times the speed of sound that would be about 400 C. The formula for stagnation temperature is the temperature of the incoming air plus 1/2 the velocity squared divided by the heat capacity of the air at constant pressure. At 400 C you will emit in the infrared but you won’t see a strong glow.
It might be interesting to think about the sonic boom or shock waves when your character goes supersonic. That might create a visible and audible signature. Also the force field might act as an airfoil, or create turbulence behind it. The shape of the airfoil would determine the lift and also probably the reaction time needed to control the flight. Turbulence might impact other aircraft.
You could also alter the shape of force field itself. Probably something like below. You may have a bright spot at the tip,but nothing that will block wider forward visibility, though I'm not sure about side curves.
This shape is just a guess based off my knowledge. It may or may not actually work. and you may need to alter exact geometry to make it efficient, and good looking.
Or you can go an easier route and copy design & geometry of a fighter jet, as far i know they don't suffer from heated air blocking their vision.
Just make your transparent forcefield be only transparent for visible light.
I.e. your forcefield allows just visible spectrum of electromagnetic radiation (380-750nm) to pass, and blocks all other wavelenghts of electromagnetic radiation. It also acts as Thermal Protection System - it's good enough for reentering spacecraft, it is good enough for your character.
(note: humanity current level of TPS technology uses mostly ablative materials for thermal protection at supersonic speeds, but in theory forcefield could be doing that)
Update: The exact limits would depend on the nature of your forcefield - i.e. what exactly does it shield against ? Convection? Conduction? Thermal radiation? None of the above? (not much of a forcefield, then). That are probably your main concerns at reasonable speeds (like being able to overtake fighter jets -- it is all another issue if you envision him going at, say, near-relativistic speeds).
Even if your forcefield does not block radiation (but only conduction and convection), note that radiation becomes dominant factor only far above hypersonic speeds (at about 12km/s / cca. mach 35). (It likely needs expensive supercomputing to simulate the radiation emitted, so it is unlikely you'd get detailed information on that. Not that nobody could tell if the shield is transparent when it is engulfed in a ball of superheated non-transparent plasma)
Also, how much does it have to follow real physics? It seems your guy has ability to pull vast amounts of energy (for forcefield, and his flying at high speeds) out of thin air, so he might conveniently also create temporary vacuum in his flight path so he is not worried at all those plasma-creating issues or other ideas. His forcefield would need to contain breathable air anyway, so that would limit the length of his flight (unless he also has ability to put more oxygen inside bubble or regenerate $CO_2$ to $O_2$).
So I'd say your guy (with good enough forcefield) could do mostly anything you want him to do, when he is put against current level of civilization (You need to do some handwaving anyway to explain sidestepping first law of thermodynamics which grants him all that energy).
He would certainly fare much better than that Santa Claus guy under similar conditions.
Additional problems of interest: he would need to accelerate and decelerate (and change direction) relatively slowly in order not to be put under excessive g-forces (unless he also has some kind of adequate inertial dampeners), and (if going fast enough) the superheated plasma would likely wreak havoc on his destination when he finally arrives there (unless he sheds it on the way somehow).