The program image is not cognizant of the speed or temperature grades, so you can use the same image on a C6, C7, C8, I7, I8, etc.
Whether the devices works as specified depends on how close to the margin (setup, hold) and clock rate you are running at.
The timing analysis report will tell you the maximum computed clock rate, compare that to what you actually run at.
Worst case setup and hold paths are also listed, you can see how much slack you have using the results from the report.
Generally speaking moving to as faster part is virtually never an issue.
If you are really concerned, you can rerun the existing layout thru the timing analysis tool with the new device speed grade.
