Your multi-meter with a type "k" thermocouple is essentially the same as a dedicated temperature meter. You can buy super fast reading replacement thermocouples if desired. The stock probe on my Cole-Parmer unit is plenty fast for my purposes. It's the response time of the probe that will vary with design, but the meters respond almost instantly. They simply monitor the current resistance of the probe. Basically it's a calibrated ohmmeter with a built in algorithm that converts the measured resistance to temperature. It would pay to shop around a little for the best price on a replacement thermocouple. Prices vary widely depending on the source.
Actually the thermocouple does not work on a resistance principle. A thermistor works this way, and an RTD, but not a thermocouple. A thermocouple is a passive device. It is a junction of two dissimiliar metals. The junction is in the tip of the probe. At this junction a current flows due to the different metal properties of each conductor. As the temperature changes the metals expand at different rates, and the amount of current that flows through the junction in millivolts increases as temperature rises and decreases as temperature drops.
Thermocouple are one of the lesser accurate types of industrial probes, but they are one of the more robust, and have a very large usable range. The junction of a type K probe is good for reading temperature to over 1000 degrees C so long as the sheath is rated that high. The base accuracy of a thermocouple is only gauranteed to 2 degrees C or 4 degrees F. In pratice though if you are not using the probe at extreme temperatures they usually stay within a few tenths of a degree. For the temps we measure in brewing they should not deviated more than that unless they are stored in a manner that allows the connectors to corrode.
The probe will not be damaged by getting wet. Unlike resistance probes that have a current sent through them by the meter to read the resistance thermocouples are passive. The current that flows across the junction is a physical property, not an electronic one. So if they get wet there is no sensor to be electrically damaged. If the connector gets wet, simply open it up clean it and dry it and it will work fine the next time you want to use it.
As to the meter. The meter must serve 3 purposes for a thermocouple.
1. It must read the millivolt voltage across the probe junction
2. It must have a circuit to convert the milivolt reading to temperature
3. It must have a reference junction compensator.
It is the accuracy of these 3 operations that determines the accuracy of the meters. Dedicated thermocouple meters generally have a much better reference junction compensation circuit. What this circuit does is this.
When you connect your probe to the meter you actually create a second junction of dissimiliar metals where you just connected the probe. Without a way to compensate for this the electronics in the meter would see an additional temperature (room temp) at the probe connector and add this to the temp at the probe. So if your room is at 70 degrees, and you have the probe in 100 degrees, the meter would report 170 degrees.
A small temp sensor in the meter monitors the temp near the probe connector and subrtracts it from the total reading, basically compensating for room temperature at the junction where the probe connects to the meter.
This is an area where a multimeter is generally a little less accurate than a dedicated thermocouple meter. The quality and placement of the reference junction sensor inside the meter case. This and the fact a thermocouple meter can concentrate just on the accuracy of measuring millivolts with circuits dedicated to that range of inputs vs a multimeter which is a jack of many trades in measuring
Also this means you should not hold the meter tightly in your hand, or you will raise the inside temp of the case above ambient air, and create an incorrect compensation temperature. It also means you should let the meter come to room temperature if it has been removed from a much different temp environment prior to use.
There you go. More than you ever wanted to know about thermocouples.
