The drain current temperature coefficient for a MOSFET depends on its inversion coefficient. In weak inversion, the drain current increases with temperature due to negative dependance of Vt on temperature, while in strong inversion the drain current reduces due to mobility degradation taking precedence over Vt decrease. The point is that even if the MOSFET was originally in weak inversion, it cannot increase forever with temperature as at some point it will be in strong inversion which will limit furthur increase. Current imbalance if it exists can only be ignorably small in paralleled MOSFETs. There is no secondary breakdown in MOSFETs to limit the SOA.