The "U" Stamp is one of several stamps that are used by manufacturers to denote that the equipment is certified as being built to the American Society of Mechanical Engineer's standards.
Although not specifically required by ASME, API RP521 strongly implies both explicitly and implicitly that one should definitely consider the air cooler a pressure vessel (Paragraph 3.15.7) and therefore provide a PSV for fire, if fire is indeed a credible scenario.
To add detail to pleckner's response, I presume that the equipment has a nameplate which was attached by the fabricator which lists things like who built it, the MAWP (max allowable working pressure), design temperature, etc. If the equipment was designed and built to ASME VIII-1 then a "U" stamp may have been applied to the nameplate, usually in the top left corner.
Just wanted to throw something else out there. When considering a fire relief case you calculate the wetted surface area based on the height of liquid that is within 25 ft of grade. Normally air coolers are located on the pipe rack and are higher then 25 ft of grade. Thus is a fire case applicable to an air cooler? I would think not?
Not necessarily so. The real criterion is 25 feet above the sustainable fire or where a pool can develop. It has nothing to do with grade in the true definition of grade. If the air cooler sits 10 feet off of a concrete floor or pad and a liquid pool can develop on this floor or pad, then that becomes the reference elevation or zero. If it is on a pipe rack and the rack is only 20 feet above grade, then it can still be in the fire zone.
