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LTC2983 running hot; incorrect "cold joint" temp

During a bench test, where a heat gun was used to increase the temperature of a type J thermocouple, reported temperature exceeded 500 C and insulation near the tip of the probe started to melt.
After this test, room temperature / cold joint has been reported by the LTC2983 as much higher than actual: in the latest test, it started at 34 C (room at 22 C), and it kept climbing.
I replaced the transistor (BC 547B) used for cold joint compensation, but there was no change in behaviour (I tried another transistor and also a diode).
I also noted that the chip is running *very* hot (hotter than "uncomfortable to the touch").
The chip overheats even if there are no probes connected .
The transistor used to measure cold joint temperature is not close enough to the chip to be influenced by the overheating. Furthermore, before this event, it always reported reasonable temps.

I presume this chips has been damaged - the question is how? 
The only "abnormal" situation is the one I described, where the probe's temperature went to ~500 C, but a J thermocouple has a range of 0 to 750 C, so this should not be the culprit...?

And even if the probe was damaged,  the LTC2983 should not be affected, given all its "defences"...



Configuration:
Arduino nano running code generated by Analog's demo software.
I have the following probes connected to the LTC2983:
Type J, grounded, differential measurement
Type J, grounded, single wire measurement
Type K, not grounded, differential measurement
Type K, not grounded, single wire measurement
BC 547B used for cold joint compensation

Thanks in advance for any help you can provide.