Even in the cool season, which runs from November to March, Bangkok can be very hot. The 'cool' season here means that SOMETIMES the temperature falls below 70 F. Because of this, try to schedule your visits to the Grand Palace and temples in the early morning, and leave some free time in the late afternoon for cooling off by the pool, or shopping in one of the many air-conditioned malls, if that's your thing. Try to schedule your visit to the Grand Palace (which includes the Temple of the Emerald Buddha) on a weekday. Two of the throne halls and the old palace armory are open to the public on weekdays, but closed on Saturday and Sunday.
Lastly, try to schedule some time to just wander around the older parts of the city, like 'Ratanakosin' - the old city area - or Chinatown. Some of the best sights in Bangkok aren't in any guidebook, they're the everyday activities and shops found on this surprisingly multi-cultural city.