AWD may be tried, but in the end, do F1 cars need any more front end understeer?
Four rear tires would definitely be interesting. At around 1500hp, I think driveline losses from the extra axle would be more than compensated by the extra grip. And think how many more laps they could go with more tires.
I see unrestricted F1 cars looking a lot like LeMans cars with longer tails. They'd have ground effects that would serve double duty. Two small ground effects fans would serve to cool the brakes on the faired front tires, one front-central fan would serve for ground effects and to cool off the cockpit. Two large rear fans would shoot straight through the radiators.
The body would resemble a McLaren F1, maybe, with a long boat-tail. Coefficient of drag would be around 0.27. In the corners, small canards at the front would swivel to increase downforce, small airbrakes would pop up over the front wheel-wells to help slow the car down and maximize the downforce and cooling effect of the front ground effects fans mentioned earlier.
The long boat tail would turn into a mulit-piece variable wing... the large area of the wing ensures a maximum disruption of the airflow behind the car, making it very difficult for other cars to tuck in behind it. The variable tilt would ensure maximum airflow over the wing, even if the car is cornering. Ferrari got some flak over apparently flexible wings before... this is the same concept taken further.
The front and rear wheels could be faired in. Changes over a couple of seasons could see the introduction of rear-steer on some cars, but the extra weight might not be worth it. Some cars may have AWD, some might have six wheels, with either double drive wheels or double steering wheels. Some may just possibly have eight. More than eight would be ridiculous, but who knows? With better aerodynamics, many teams may drop the fairings, as they make wheel changes difficult.
Gas turbines are too fuel-hungry. The car still needs to do between 35-70 laps. I'd bet on a turbocharged small-capacity V6 or V12, or maybe even rotaries (they don't have to last more than one race). Engine output would be around 1200-1500hp... but if the series lasts into this decade, 1700-2000hp wouldn't be so far-fetched.
Oh, cars would have traction control, ABS, EBD and everything else. Engine management programs could be programmed to adapt braking and rev-limiters to various corners and tracks (I know this has been experimented on). Plus complicated systems to control the variable tilt aerodynamics and ground effects. Pilots could have aero-switches, that would allow them to increase wing effect in corners to create enough turbulence to make things very uncomfortable for opponents behind them, or to make the car as sleek as possible in the straights, eliminating drafting.