I am fascinated with feedback control systems. They always grab my interest. I'm in awe of the way something in the physical world can be expressed by a few simple equations. This is true for something as simple as a device failing by overheating because of a positive feedback loop.
The temperature rise of an actuator coil driven with a current source may result in thermal runaway and is governed by a few simple equations. The loop gain can be derived for the system suggesting design limits to prevent thermal run-away.
These are the simple mechanisms of self heating:
- Current dissipates power
- Temperature rise is proportional to power,
- Resistance increases with temperature
These three elements form a positive feedback of power to temperature and can be analyzed using small signal partial derivatives. The three equations are combined to yield  
This should be recognized as being the form of a positive feedback system. The forward gain is the numerator and the 2nd term in the denominator is the loop gain. Positive feedback is evident from the negative sign in the denominator.
The stability is a function of the RMSÂ current, thermal resistance and resistance thermal coefficient. The plot below is an example of a actuator coil temperature rise versus current given a Cu coil with initial resistance 10 ohms and a thermal resistance of 30 C/W.
The loop gain is only about 5% at the highest current shown in the graph.
Always keep in mind the operating range. Some parameters, such as resistance, may be non-linear at extreme temperatures.