When it's very hot out and you do not have air conditioning, it's difficult to do any job at the office, but there are ways to get cool and remain cool long enough for you to keep working.
The way to tell that you are perspiring is rest one body part upon another, whether it's your head resting on your hand, or your bare legs resting against one another. Take away the resting body part and if you're soaking wet, you're losing fluids quickly.
A fan is a good choice.