The MOSFETs aren't changing from PTC to NTC. Many MOSFETs that I've used exhibit this behavior and once you know why, it's super simple. MOSFETs have 2 separate characteristics to consider, the gate-source threshold voltage (VGSth), and the drain-source on resistance (RDSon). The VGSth has a NTC slope while the RDSon has a PTC slope.
If you're building a switched mode power supply, where the FETs are always either fully on or fully off, then your devices will operate primarily with a PTC slope and you can usually completely ignore the VGSth aspect of the device. This would probably apply to Class-E RF switching PAs as well, but I only have experience with SMPSs as far as switching applications go.
Now, since we're building linear PAs here, we're operating the MOSFETs in their linear region and with quiescent bias current following. In this case the NTC slope of the VGSth is very important and it is why you need thermal tracking bias circuitry to keep these devices from going into thermal runaway. If you hold a constant bias voltage on the gate of a MOSFET it will draw more current as it heats up.
The slopes of the two different characteristics have differences in how steep they are, if they are curved or not, and in some devices they even cross at a certain temperature. If they cross, this will usually cause the effect described above. Below a certain die temperature, the PTC effect of the RDS will be dominant, then as the temperature rises, the NTC effect of the VGSth will rapidly overtake it since it's slope is usually much steeper.
I don't have much experience with LDMOS devices, but I've built many SMPSs and I've home-brewed quite a few linear PAs with both switching FETs and VDMOS RF FETs, and they behave completely opposite in the two applications. I haven't encountered too many devices where the slopes crossing has been a problem, but it can cause issues when trying to stabilize a biasing circuit, depending on the crossing temperature.
If I can locate the PDF file of the article that first clued me in to this weird behavior, I'll attach it. I'm not sure where it's saved at. I do remember having a conversation about this in another thread a long while back though. Hope this helps to explain what might at first seem impossible.
Brad - KC3MOP