The information of the Quark's Watchdog Timer can be found on the section 21.14 of the Intel® Quark SoC — Datasheet in case you want find more information about it.
That being said, I believe what you are trying to do can’t be done. Since a Watchdog timer is directly related to the main processor and not to the OS’ processes.
What am I trying to say? What I’m trying to say is that if an Arduino sketch hangs it doesn't mean that the whole system is hanged. The Watchdog timer looks at this and considers it a normal operation of the processor, since it is only a tiny portion of the system that is on a hanged state. On the other hand, if a process makes the whole OS to crash, the Watchdog timer will recognize this and reboot the board.
@Intel_Peter Is there any way to monitor a particular process status(running properly or crashed).