The temperature at the very centre of the thickest part of the food.
Measuring the surface temperature is not enough. To prove food is safe, you must probe to the core. In Ireland, the standard target is 75°C instantaneously, though equivalent combinations (like 70°C for 2 minutes) are legally acceptable if validated.
No, that is impractical. However, you must perform and record "monitoring checks" at critical intervals. For example, check the first batch of the day, and perform random spot checks during service. If you are hot holding food, you should check and record the core temperature (above 63°C) at least once per service period (e.g., AM and PM) to prove due diligence.
For thin products, you should insert the probe from the side into the thickest centre point, rather than from the top down where it might touch the grill surface and give a false high reading. Burgers specifically are a high-risk item for E. coli O157; failing to reach a core temperature of 75°C (or 70°C for 2 minutes) is a primary cause of food poisoning outbreaks and regulatory enforcement.
75°C represents the standard "instantaneous kill" temperature recommended by the FSAI. However, you can legally use lower temperatures if you hold them for longer periods (Time/Temperature combinations), such as 70°C for two minutes or 65°C for 10 minutes. If you use these lower combinations, you must be able to prove to an EHO that you are consistently achieving the required time, not just the temperature.