Correct. The programming files themselves have no knowledge of the speed and/or temperature grades of the devices. The physical silicon die in each device is the same, whether the device is labeled I6 (fastest industrial temp) or C8 (slowest commercial temp). What differs is the process parameters, which determine how Intel/Altera can test and label each device to meet the required spec.
The issue to watch out for in switching between commercial and industrial temperature ranges, or slower vs faster speed grades, is the environment that your product is expected to work in:
Does your product always operate in commercial temperature range? Or does it require operation in the industrial range?
What is the clock rate of your design? How much timing margin is there? Are you clocking it at a rate such that only a faster speed grade device will work over the full design temperature range?
Only you can answer these questions.
You can always go back to Quartus and change your device spec from say, I6 to C8, and based on the clock rate you supply, does Quartus timing analyzer still pass? Or does it now generate setup errors or maximum clock rate exceeded errors?