Bob: Thermistors are cheap, simple, and can be fairly robust (glass bead). Their main faults, nonlinearity and poor long term stability, are not important to this application. As it turns out, the design of a protective sheath is critical to this application - and NOT just for physical protection of the sensor element. Ash is a very low conductivity, low thermal mass material. The ratio between the thermal mass of the probe element (weight x Cp) and the area exposed to the ash is a critical parameter. A bare sensor has the lowest possible thermal mass, but also has very little area in contact with the surrounding ash. The ideal sensor/sheath would be physically robust and have a large its area to weight ratio. It doesn't really matter to the uP or code how the signal is generated.
Paul: As you guessed, once the alarm conditions are met, the alarm will sound for a fixed period of time - a second or two at a minimum. The alarm will continue to sound as long as the alarm conditions exist. The alarm condition exists whenever the rate of rise exceeds a certain value OR the sensor temperature is above some absolute value.
Imagine the firefighter sweeping the sensor "near" a localized hot spot (near depending on how hot the spot is and how thermally conductive the surrounding material is). The rate-of-rise condition alarm would be met and the tool would alarm (beep, LED, vibrate) for a second and then go silent as the probe moved back into cooler ash.
The abrupt termination of the alarm would prompt the firefighter to move the probe back toward where it was when the alarm sounded. Think of playing the game "hotter - colder". If there is a "real" hot spot (temperature high enough to act an ignition source: >~300C) there, the firefighter will locate a spot where the absolute temperature of the sensor exceeds the a threshold and the alarm sounds continuously.
The firefighter doesn't really need to be able to turn off the alarm at that point. He just removes the probe and gets on with the job of digging out and eliminating the problem.
I would appreciate any help you can provide, my email address is in the first post.
OH, neither Centigrade nor Fahrenheit. It's all just "counts" as produced by the A/D. The conversion (calibration) COULD be done (dependent on the probe/sheath design, thermistor characteristics, linearity correction, etc.) but is not really useful for anything. It all just boils down to A/D counts in the end. That being said, my current prototype (8 bit conversion, linearized 10K thermistor, room temperature) has a LSB resolution of about .2 deg C - which appears to be more than adequate.