I fuse glass and have a ceramics friend I set up exactly this for, so I’ve been through the shopping list.

Measurement: use a MAX31856 breakout instead of the MAX6675. It reads K, but also R and S, and handles the full range. For a kiln going to cone 10, an S or R type probe in a ceramic (alumina) protection tube is what kiln makers fit themselves. It’s pricier than K but doesn’t drift the way K does at 1250+. If you stay at cone 6 most of the time, a heavy-gauge K in a ceramic sheath is acceptable, just plan to replace it. Mount the probe through the wall at the same depth as the kiln’s own one so the two readings compare.

Send it as kiln_c every 30 s or so, plus kiln_fault from the MAX31856’s fault register.

Alarm rule on the profile, written in JSON mode because I wanted dampening defaults kept and two severities:

{
  "type": "kiln_overfire",
  "title": "{{device.name}}: {{value}} °C",
  "severities": [
    { "severity": "CRITICAL", "condition": { "key": "kiln_c", "op": ">", "value": 1290 } },
    { "severity": "MAJOR", "condition": { "key": "kiln_c", "op": ">", "value": { "attribute": "max_c" } } }
  ],
  "debounce": { "mode": "count", "raise": 3, "clear": 3 },
  "hysteresis": 15,
  "enabled": true
}

max_c is a device attribute you change per firing (1240 for cone 6), so a normal firing never touches it. The CRITICAL line is the «something is very wrong» ceiling. Three readings in a row means a noisy spike won’t wake you. See Debounce, hysteresis and dampening.

«Stays hot too long» can’t be done in a profile alarm rule since it can’t track time since the firing began. I used a Rules card with a value trigger «rises above 600 and stays so for» 720 minutes, then notify.

And keep a real over-temperature cutout in the kiln’s power circuit. The cloud tells you, it can’t open the contactor if the Wi-Fi is down.