Since you are referring to a ring, I assume it is a 2D problem, although, it could, at a cost, be extended to a 3D problem.
I also assume that, in method 1, you are talking about one heating element installed in the middle of the ring of thermistors. If this is not a correct assumption, I would consider this approach anyway.
Again, assuming a 2D scenario, you could use a PCB to place and wire all your devices. Method 1 structure could look like a clock:
For the best operation, the heating element in the middle should be thermally insulated from the sensors (i.e., no copper plane), so that most of the heat transfer is done by the moving air, not by the board. To further improve the insulation, you could remove some of the PCB material between the heater and the sensors (white ring on the drawing).
The sensors around the ring should also have minimum thermal contact with the PCB, to minimize their thermal mass and make them more responsive.
You can use thermistors or many other types of temperature sensors.
I believe that method 1 should be more efficient than method 2, because you can use just one heating element rather than multiple heating elements, i.e., one for each thermistor.
Method 1 should be more accurate, since you would not have to worry about all heating elements having the same initial temperature and, most likely, you would not need any calibration.
With method 1, you would not need any pipes to direct the air flow.
You can control the sensitivity and resolution of your device by changing the number of sensors, the radius of the ring and the temperature of the heating element.
In summary, method 1 seems to be better: more efficient, more accurate, easier to implement and operate.