Can you take water with you also and something like an aluminium pie dish to put it in, then place in the shade? Well done on trying to help this cat and not shrug it off. My Willow chose me at the shelter, not so much by coming up to me since she's a shy social feral, but she kept sitting near me, staring up into my face and then watching me move around the room. She was very quiet, but very determined.