It could well be the fan motor, its sensor, or its relay. when the temp reaches normal or slightly above the fan should run, it should also run when you first turn on A/C. When the car is cold, remove the rad cap, to see if it is full, run a while with cap off if your worried about air locks, you can normally see the coolant circulating .Water pumps normaly leak when nackered.
just to add, i once brought a fan motor from Nissan lasted only 15k klm 6k baht ! Brought an after sales motor from GT battery shop still works after 3yrs 2k baht.