this sounds like either a shim or other noise fix is missing, if this is the case then check if there is any difference from side to side or see if the caliper should have shims (im sorry i dont know for the a3, only thats its pretty likely that they have them).
however you say its occuring off brake so its more likely to be....
It sounds like for whatever reason the pads aren't knocking back like they should, first thing i would look at it greasing the slider and the pins, since its most likely the outboard pad causing the noise. i would also try applying some grease/ copper slip to the ears of the pads (the part of the backplate that hooks into the anchor to locate the pad). possibly worth checking the handbrake mechanism )possibly wind it out) too before taking the plunge on saying its the piston. i only say that because its the most expensive bit and so the last thing i would try if it was my car.
if the pad isnt knocking back then it makes sense that the noise will be worse when hot.
im afraid thats all the advice i have - good luck!