I cleared every mod apart from NF electrical and did some tests:
4 identical craft (in this case rovers, RoveMate core and some wheels) with an MX-3S FLAT reactor and a single small radiator to cool them. Not nearly enough to cool them at full power, but I didn't go anywhere near full power!
Rover 1- start the reactor, get it up to temperature then set power to 1%. It sits quite happily at 900K with that one little radiator.
Rover 2- as above but set the reactor to 0% when it's warmed up.
Rover 3- start the reactor and set it to 1% immediately, without letting it warm up.
Rover 4- start the reactor and set it to 0% power immediately, still cold.
Time warp for a while- initially I tried 30 days at full speed, but it turns out just warping to the next morning is enough.
When I came back, rovers 1 and 2 were absolutely fine, the reactors were still at 900K and fully functional. Rover 4 was also fine, the reactor was at ambient temperature (290K or so).
Rover 3, on the other hand, was at 11,000K and core health dropped from 100% to 0% in less than a second after selecting it. Shortly afterwards the reactor exploded from overheating...
After removing what was left of Rover 3, I turned the power on 1 and 4 up to 5%, which is too much for the single small radiator to cope with, then fast forwarded for a while again. When I came back to them, they were both sitting at about 1300K, which triggered the emergency cut-out (I set it down to 1300K instead of the default 1350 which will cause reactor damage) and turned them off with no damage done. No meltdowns.
I tried various combinations of reactors and radiators and found a pretty similar picture- a cold reactor at low power settings will spontaneously melt down if you time warp for a sustained period, if it doesn't have enough active cooling to keep it cool at maximum power. An MX-3S melted down at 1% power even with twelve large radiators stuck on it (the only other part on that vessel was a probe core) and sticking one of each reactor to a 6-way station hub with around 20 large TCUs attached to them and leaving them cold at 1% caused many meltdowns.
I tried a test with two MX-3Ls stuck together, each with one large radiator attached and a probe core to control it, no other parts. One was started and warmed up and the other was started but kept cold. (By this point I finally remembered how to do screenshots in forum posts so there are some screenshots below, hope they help!)
At 3% power (which it can run at quite happily, the radiator is just enough to keep it cool) when I warped to the next morning the hot reactor was absolutely fine but the cold reactor had melted down and was at 12,000K.
At 4% power, which is slightly too hot for one radiator to manage on its own, it was a similar story: hot reactor OK, cold reactor catastrophically overheated.
At 50% power, things are a little bit different- the hot reactor hit 1600K despite the cut-out temperature being 1000, but the cold reactor still hit 10,000K and melted down.
At 100% the hot reactor only hit 1200K and the cold reactor was a mere 7600K...
I also tried turning the reactor to full power with no radiators at all and setting the cut-out temperature to 2000K then fast forwarding while still controlling the vessel, but the reactor melted down at about 1900K and didn't come remotely close to 12,000!
To conclude: starting a reactor at any power level above 0% but leaving the vessel and time warping before the reactor has warmed up will almost certainly cause it to catastrophically overheat and melt down when you come back to that vessel, unless there are enough radiators on that vessel to dissipate the heat produced by the reactor at 100%. A hot reactor doesn't do this regardless of radiators or power setting.
During these tests I noticed that melted down reactors can be switched on again, and they will continue to use uranium and produce depleted fuel despite making zero power. Is this supposed to happen?