I've designed and installed a lot of ambient vaporizers - including nitrogen, oxygen, and argon. All these involved liquids in the cryogenic zone (less than -150 oF). All cryogenic vaporizers will do exactly that: vaporize a saturated liquid at the saturated temperature related to that fluid. However, the excess heat transfer area given to the ambient vaporizer coil allows for post sensible heat transfer as well as the basic latent heat transfer and this causes the final end product to exit the coil at close to the existing ambient temperature used to effect the basic vaporization. In humid climates - such as here in Houston, Texas - it is not unusual to have the ambient vaporizer coils coated with water ice (subcooled to cryogenic temperatures) and the deposition of this hard ice forms an efficient insulation around the coils, lessening the effective latent heat transfer area and, subsequently, decreasing the total heat transfer available - both latent and sensible. This would apply to both natural or forced circulation ambient vaporizers. Most cryogenic vaporizers I've found today are of the natural circulation type, with a generous excess heat transfer area. This is considered much more practical than furnishing and maintaining an air ventilation system.
Therefore, what ultimately happens, if the coil does not have sufficient excess surface area, is that the exit gas temperature starts to decrease. Experienced cryogenic vaporizer designers such as Air Products, Praxair, etc., know this and provide the empirical coil area necessary for the process and the ambient environment involved. The coldest cryo fluid I've vaporized is liquid hydrogen and the exit temperature from my vaporizer varied - but hardly ever got lower than 20 oF below that of the ambient air - as Zauberberg has noted.