I have a propane fired boiler. The Microtemp Fuse Limit STC5300 G4AM0600 152C Thermal Cutoff Switch, which is a heat-sensitive fusible link, has failed. The cause was the flame from the burner area was spreading out into the controls area; (I know that that is the purpose of this part.)
There was also an L340F limit switch, positioned in the air intake, that was tripped. I believe it is the manual reset kind, and in the process of troubleshooting, I suspect I reset it. (It had no continuity when I first tested it, but after I removed it, it had continuity.)

The burners have a coating of soot/carbon, which is probably related to whatever caused the flame to spread out of its proper location.

Carrier?
Boiler Model # BW2AAN000105ABAA
Series # PWB-4D
Serial # 4704V08476