What other familiar systems have a "runaway" behavior like the auto trim?
It didn't runaway. The pilot made such high nose-up demands via the SS for such a long time that to satisfy his demands the system gradually trimmed to full nose-up. If he'd relaxed the back pressure for long enough (ie. taken "standard" stall recovery actions) the trim would've moved back towards the nose down position. It just trimmed to try to satisfy what the pilot what was asking of it - a high nose up attitude.
If I turn the thermostat up on my heating system I wouldn't expect the temperature to get hottor and hotter indefinitely
No, but if you set the thermostat to a temperature that was higher than the heating system could achieve the temperature would rise to that limit. Similarly, the pilot was requesting a nose-up attitude that the aircraft, with it's low speed, couldn't achieve and the trim ended up moving to the nose-up limit.