Like Martin, I believe cooler is better. Hotter, I also believe, reduces the life of electronics. So much so, that going above spec temperatures, is what causes premature hardware failure. (BTW, temperature to operational life might be on an exponential curve.)
The "ideal" temperature, for the equipment, is probably 0C, but 20C, besides being in the middle between 0C and 40C, is about just right for people too.
But to your customer's goal, something else to consider is temperature where?
Temp. specs really means inside the device, across all component electronics. Ideally, device's design insures no hot spots in the device, but something as simple as leaving an empty module slot (i.e. no cover plate) can disrupt the internal airflow. Or not having the ideal air flow to or from the device (i.e. external to device local hot spots). Running in a max temp. situation, leaves no margin for error (another advantage of staying below the max temp. operational value). (Keep in mind, if internal airflow isn't as "expected" device may not trigger a over temp alarm when some of it is over temp.)
So, with a real careful review of airflows to/from device, and device hardware configured for internal airflow, yea, you can probably push up to even the max, like 40C. Again, this leaves no room for error (or a reserve cushion, as noted by Reza), and possibly shortens the life of the equipment. (By shorten, though, if you stay within spec, you'll likely achieve the design life of the device, but perhaps not the extra 5 to 20 years some equipment remains in service beyond that. [Whether the last is a good or bad thing is a different debate - laugh.])
