How much power can a thin wire handle before heating too much?
Skin depth at 3GHz is only 1.2um, you'll need to consider that. I have no idea if this calculator is accurate, but it gives a resistance of 18.8 ohms for 100mm of straight 25um wire. However AWG 30 is more like 250um (0.25mm), so which is it?  It would be more like 1.8 ohms for 100mm of 250um wire. Note that at 3GHz and this kind of diameter, the resistance is roughly proportional to the reciprocal of the diameter rather than the reciprocal of the diameter squared, since it's only a thin shell around the outside that's doing all the work. 

In the case of 250um, that's about 50x as much resistance as the wire exhibits for low frequencies. 

AC resistance will let you calculate the power dissipation, but calculating the temperature rise will not be easy- there may be tables used by transformer designers (since large transformers are often immersed in oil) but I doubt they go down to 250um let alone 25um.