Short answer
Water of 180 oF (82 oC) causes immediate scalding (thermal burn wounds).
Background
The severity of a scald injury depends on the temperature to which the skin is exposed, and for how long. Residential water heaters warm up tap water typically to 120 oF (48 oC). At this temperature, the skin of adults requires an average of five minutes of exposure for a full thickness burn to occur. When the temperature of a hot liquid is increased to 140 oF (60 oC)) it takes only five seconds or less for a serious burn to occur. Coffee, tea, hot chocolate and other hot beverages are usually served at 160 to 180 oF (71 - 82 oC), resulting in almost instantaneous burns that will require surgery (American Burn Association).
How these numbers apply to steam I am not sure, but I think they will be comparable, given that steam is essentially made up of a dense mass of water droplets. Further, the amount of steam obviously matters. Consider these numbers: The temperature in a sauna typically ranges from 160-200 oF (71 - 93 oC) with a low level of humidity (ranging from 5 - 30%). Steam rooms provide moist heat from a water-filled generator pumping steam into the enclosed room. The temperature in a steam room typically ranges from 110-114 degrees Fahrenheit (43 - 46 oC) with a humidity level of 100%.
There is anecdotal evidence of the Russia-born Ivan Ivanitz Chabert (1792-1859), who supposedly entered an iron oven in Paris with a few trays of meat, and stayed there unscathed for 5 minutes at a temperature of 380 degrees F (193 oC). When he re-emerged from the oven the meat was cooked, while the only noticeable effect on him were profuse sweating and a dramatic increase in heart rate (from 98 to 168 bpm).
This experiment shows the remarkable capacity of the human body to reduce overheating by means of evaporative cooling (sweating). However, the effects of steam are far more devastating to the human body than dry heat. Not only does it carry much more energy than hot air, it also prevents perspiration by saturating the air with water vapor.
References
- American Burn Association Educator's Guide