How hot can an iPhone get before displaying a temperature warning?
TL:DR - Don't leave it in the sun. Especially face up with the black display (and pobssibly bezel) exposed to direct sunlight.

From Apple KB:  


  Keeping iPhone, iPad, and iPod touch within acceptable operating temperatures
  
  Learn about the operating temperatures and temperature management of iPhone, iPad, and iPod touch (4th generation and later).
  
  Use iOS devices where the ambient temperature is between 0º and 35º C
  (32º to 95º F). Low- or high-temperature conditions might cause the
  device to change its behavior to regulate its temperature. Using an
  iOS device in very cold conditions outside of its operating range
  might temporarily shorten battery life and could cause the device to
  turn off. Battery life will return to normal when you bring the device
  back to higher ambient temperatures. Store the device where the
  temperature is between -20º and 45º C (-4º to 113º F). Don’t leave the
  device in your car, because temperatures in parked cars can exceed
  this range.
  
  Your device might get warm
  
  When you use the device or charge the battery, the device might get
  warm. You might notice that your device feels warmer in these
  situations:
  
  
  When you set up your device the first time
  When you restore from a backup
  When apps reindex or reanalyze data, like Photos tagging for faces, places, or keywords after a software update  
  
  
  These conditions are normal, and your device will return to a regular
  temperature when complete.
  
  Here are some of the higher ambient-temperature conditions and
  activities that might cause the device to change performance and
  behaviour:
  
  
  Leaving the device in a car on a hot day.
  Leaving the device in direct sunlight for an extended period of time.
  Using certain features in hot conditions or direct sunlight for an extended period of time, such as GPS tracking or navigation in a car,
  or playing a graphics-intensive game.
  
  
  If your device gets too warm
  
  If the interior temperature of the device exceeds the normal operating
  range, the device will protect its internal components by attempting
  to regulate its temperature. If this happens, you might notice these
  changes:  
  
  
  The device stops charging.
  The display dims or goes black.
  Cellular radios enter a low-power state. The signal might weaken during this time.
  The camera flash is temporarily disabled.
  
  
  Additionally, if you're navigating, the device might show this alert
  and turn off the display: "Temperature: iPhone needs to cool down."
  Navigation still provides audible turn-by-turn directions. When
  approaching a turn, the display will illuminate to guide you through
  the turn.
  
  If you see a temperature warning screen
  
  If the device exceeds a certain temperature threshold, it will present
  a temperature warning screen similar to this:
  
   
  
  An iPhone showing this message might still be able to make emergency
  calls.  
  
  To resume use of your device as quickly as possible, turn it off, move
  it to a cooler environment, and allow it to cool down.