60C is fine for that card (97C is the max temp for that card). As long as it doesn't get much higher you should be alright.
Will the temps go down if I put a fan in the case?
Yup, depending on where you place that fan it should help with the temps. It really depends on the case but a good spot (if possible) is to mount a fan on the side panel of the case blowing cool air in onto the card. That will help cool that card significantly but anywere you place one im sure will be fine. If you have to place the fan on top or rear use it to exhaust hot air from the system.