More than likely thermostat is not working and thats why engine jacket is holding up hot water than circulating thru radiator as thermostat is a gate keeper and open and close when it sense the water temperature is high. get that change and it be fine. Hopefully.
Thats why its overheating after 15 mins, as when car is cold, the water in the engine jacket take 12-14min to reach idle temp to switch thru radiator and thats why after 15th min it show overheating signs. Its all my assumptions but more than likely it is the problem.