Dear witsend,
I presume that her grandfather, and also your friend, are both medical doctors, otherwise you would not be seeking medical advice from them. As to the lead levels, were these checked by yet another doctor? Your best course would be to ask your family physician if there is anything wrong with your little girl.
The excessive heat we have been experiencing this summer may have something to do with her hot head but I would never say that it is common for young children to have hot and sweaty heads. For your own peace of mind, and to avoid some serious consequences of ignoring the symptom, you should clear this right away with your family doctor, and then you'll enjoy the rest of the summer.
Yours sincerely, GG