gentle turning of the car

Hello, I cant figure out how to calculate angle for wheels to make car turning smooth. Arleady I have somethnink like this:

          //Bus or car:
         if (car.VehicleTyp == 2)
         {
             angletimes = 30;
         }
         else
         {
             angletimes = 20;
         }
         //calculate angle to next path:
         Vector3 targetDir = path.transform.position - transform.position;
         Vector3 forward = transform.forward;
         targetDir.y = forward.y = 0;
         float angletemp = Vector3.Angle(targetDir, forward);
         Vector3 cross = Vector3.Cross(targetDir, forward);
         if (cross.y > 0)
         {
             angletemp = -angletemp;
         }
         //making turning bit smoother;
         if (angletemp > angle)
         {
             angle = angle + angletimes * Time.deltaTime;
         }
         if (angletemp < angle)
         {
             angle = angle - angletimes* Time.deltaTime;
         }
         if ((angletemp > 0 && angle < 0) || (angletemp < 0 && angle > 0))
         {
             angle = 0;
         }
         if (angle > car.MaxAngleOfSteer)
         {
             angle = car.MaxAngleOfSteer;
         }
         if (angle < -car.MaxAngleOfSteer)
         {
             angle = -car.MaxAngleOfSteer;
         }
         car.Angle = angle;

And it act like this:

But on long turns this is very unnatural. How can I make car turning like this but that it would also be made on sharper turns without delay with the possibility of maximum wheel turning?