The base die is the same, for example, for a 10M08S part, so you can use the same programming file for any speed/temp combo.
The temperature grade and speed grade are functions of how Intel tests the device and the process yields they get, combined with customer demand.
So you don't in general need to rebuild the design if you substitute a different speed/temp grade.
That being said, it also depends on how you use the part.
Are you running at maximum clock frequency?
At your clock frequency does your design timing report show close to zero margin on some logic paths?
Are you using the full operating temperature range, specifically at the high end where timing performance degrades?
So the fact that you can reprogram any speed/temp grade of a particular die with the same image file needs to be qualified.
How you use the part in your application also matters.
If you are moving to a faster part, or wider temperature range part, likely it will work no question.
If you are moving to a slower part, or narrower temperature range part, it depends on how you use the part in your circuit.
