ThermoPro TP-20 Wireless Meat Thermometer

Yes, the probes can be left in the meat during smoking. Then you can keep track of the cooking process while drinking a cold one and watching the game.

There is an alarm when temp goes above the setting. There isn't a low setting, so therefore no alarm for that.

As long as you don't hook the monitor on the handle of the pot. The plastic and silicone will melt if it rests that close to the flame. I've deep fried multiple turkeys using this temp probe.