Because of the way that Air cooling works, the temperature of your GPU will rise as the air temperature inside your case rises closer to the temperature of your card.
The temperature can never really be below the ambient air temperature of the air surrounding the card. 60 Degrees as idle is okay, as long at the temperature under full load doesn't breach 85 Degrees. Some cards are happy at 90-95 Degrees but this is pretty hot.
If this is an AMD card, you should be able to control the fan speed in Catalyst Control Center, allowing you to give additional cooling to the card manually.
My HD7870 sits around 40 Degrees idle (before I play a game) with the fans on auto (Around 20%) 70ish under full load and will drop back down to 50ish idle. My fan speeds never auto increase at these temperatures. Forcing the fan speed to 100% makes a little bit of noise but can drop my temperature to under 30 Degrees sometimes.
There should be an nVidia equivalent, but I haven't used a nVidia card since the 8600GT
Depending on the age of the card the thermal paste may need replacing too.