The critical temperature range for digital thermometers with external probes typically spans from -50°C to 300°C (-58°F to 572°F). This range allows these thermometers to be versatile tools for various applications, including cooking, industrial processes, scientific research, and environmental monitoring. The lower end of the range, around -50°C, is suitable for measuring extremely cold environments, such as freezers or cryogenic applications. The upper limit, around 300°C, accommodates high-temperature scenarios like grilling, baking, or certain industrial processes. 
The specific range can vary depending on the design and intended use of the thermometer. Some models may have a narrower range tailored for specific applications, such as food safety, where the range might be more limited to typical cooking temperatures. Others might be designed for broader industrial use, requiring a wider range to accommodate diverse conditions.
Accuracy and response time are also critical factors in the performance of digital thermometers with external probes. High-quality models offer precise readings with minimal error margins, often within ±0.5°C (±0.9°F), and provide quick response times to ensure real-time monitoring. The materials used for the probe, such as stainless steel, are chosen for their durability and ability to withstand extreme temperatures without degrading.
Overall, the critical temperature range of -50°C to 300°C ensures that digital thermometers with external probes can effectively serve a wide array of temperature measurement needs across different fields.