Yes, the birds will feel the heatup of tissue caused by the radio waves; although with today's low-powered Wx Radars the birds would have to be pretty close to feel it... probably so close that you'll have hit them anyway. Different story however with older, high-powered antennae or military hardware.
Another nice story there, BelArg, thanks for that. I enjoy your anecdotes that crop up every now and again!
Smithy