Translation:You will be very thirsty because of so much talking on the phone.
No one mentioned the possibility of "... en la telefonon" (into the phone). That's probably the most literal and accurate. From how I've come to know ĉe, I wouldn't use it to indicate the use of a phone. Also, I do view a phone as a tool (not unlike a televidilo ... Both of which I find myself standing on to use), so per seems like a good 2nd option to me.