Stability of LEDs from thermal runaway
LEDs in serious applications should (must) be driven in constant current mode.
There is then no prospect of "runaway". 

The issue then is whether the LED die temperature is maintained at an acceptable level.   Reputable LED manufacturers provide a very large body of data re thermal aspects. 

Heat sinking is the main area of attention and this is a well understood discipline. Once designed an LED mounting system will generally work as designed if manufactured correctly. LEDs are usually operated substantially below levels where active temperature management is required (ie altering power to control temperature is not a usual design practice).

..... Luxeon Thermal design using power light sources
.......... and LUXEON Thermal Management Capabilities 

...Cypress - Thermal Design Considerations for High Power LED Systems

.........ECN LED thermal design

....Digikey Practical LED thermal desigm

Wikipedia Thermal_management_of_high-power_LEDs 

Example  only - heatsinks



CFD model of thermal transfer from an LED bulb.
See Wikipedia reference above for GIF animation of this.