It depends. Some amps don't seem to care, others go thermal quickly. What amps?
Most manufacturers recommend NOT doing it, but I have done so MANY times without any issues (I had a punch 200ix shut down once like that, but it was running at 2 ohm mono, and jamming full out for a 4 hour drive- yes, it was hot as ****).
I ran a generation 2, pre HD, Punch 150 upside down mounted directly to the rear deck in my 1996 Ford Thunderbird from 1996 to 1999 and it NEVER shut off on me! I had a daily 1 hour each way commute to work! I abused some Savard HiQs @ 4 ohms stereo on a daily basis until I purchased a 12" Solo-baric which I ran @ 4 ohms mono! That amp and sub are still going strong in another friend's vehicle!