Product review (5 stars): Great part -- pity that it's needed...
Did the trick. There are a couple of other similar (identical?) products available -- quite a few reviews are available for the 'Whirlpool 9759242 Thermostat'. The bottom line is that there is a common theme -- this thing tends to fail with a "self-cleaning" cycle and, once it fails, it can't be reset -- it requires replacement. One curve-ball that I didn't pick up on from the other reviews: on our Whirlpool double-oven, there is a second thermal fuse linked to the control panel. I had the pleasant experience of discovering (eventually...) that both fuses had blown when we ran a "self-cleaning" cycle and, thus, both needed replacing (there are a couple of different versions of the thermal fuse for the control board -- I ended up using the "Whirlpool 4451042 Thermal Fuse"). Needless to say, I'm less than impressed and would steer clear of the Whirlpool brand in the future... Unfortunately, if you're reading this, I suspect it's too late to suggest that the "self-cleaning" feature is probably better thought of as something more akin to a "self-destruct" feature.