I can not see the heater delay from the trun on transients shown in the link (have not checked the whole long thread
though). It seems the supply is coming up too slow to get an instant temperature reading.
One can estimate the delay for the heater from the dimensions: from the die picture the distance from the heater (outer ring) to the sensor is about 1 mm. The thermal diffusivity for silicon is at 87 mm²/s - so expect a little over 10 ms as a dead time before power from the heater to reaches the sensor.
The PI adjustment rules (e.g. Chien, Hrones und Reswick) want the time constant in the PI regulator to be something like 2.3 - 4 times the delay for good reaction to disturbance.
From my experiance shorter can lead to instability, while longer slows down the response a little. The thermal layout external to the chip would not effect the delay very much, It can effect the best gain factor for the regulator. Even there is mainly changes the heat loss and not so much the heat capacity, which is the main factor effecting the permissible loop gain.
So one should expect a suitable time constant somewhere in the 50 ms range. Shorter may be problematic, a little longer is more on the safe side.
The LTZ1000 standard circuit calls for 100 nF and 1 M and thus 100ms , which sounds like a good, safe start and about right.