> In case (1) I was considering a Thermal IR Camera but price is still 
> excessive for me even for low-end models

Can you rent ? You might find it more economic in the long term

> Case (2) approach is the reason for which I have asked for the PIR
> sensor: walking with the PIR looking in ahead, and wait it triggers (a
> led or a sound) when sensing a temperature difference

You'd need a pretty good (Fresnel) lens for detection at 600ft, plus
all the intervening air currents and sensor movements would be quite
disruptive

Another issue is the orientation of the sensor. PIR sensors have two
piezo bars. In horizontal orientation it's like an =. The sensor's built-in
amplifier outputs a difference signal, as first one bar detects PIR, then
the other, as a body moves across the field of view. The maximum
output is when movement is perpendicular to the bar's orientation. ie
a = orientation will best detect vertical movement. That suggests you'd
need more than one sensor, in various orientations, to get maximum
response if you expect these air movements to be at unknown angles
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