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The phrase "a core temperature of" is correct and usable in written English.
It can be used in contexts related to science, medicine, or any discussion involving temperature measurements, particularly in reference to the internal temperature of an organism or system.
Example: "The patient was admitted with a core temperature of 39 degrees Celsius, indicating a possible fever."
Alternatives: "an internal temperature of" or "a central temperature of".
Exact(56)
We studied adults (n = 15) and children (n = 16) who developed mild fever, a core temperature of at least 37.8 degrees C, after cardiopulmonary bypass.
He cites the example of a man immersed in the North Sea who suffered a core temperature of 82F - 16F below normal body temperature - and could still talk rationally.
Adequacy of rewarming was assessed by measuring the coldest postoperative core (tympanic membrane) temperature and the time to rewarm postoperatively to a core temperature of 37.0°C.
The shrimps were heated to a core temperature of 72 °C in a brine solution using a small batch ohmic heater.
This study was designed to examine the impact of three hours of cardiac arrest at a core temperature of 20 °C followed by reanimation of peripheral nerve function.
During an epidemic of cholera, it is important that all food including leftovers be thoroughly cooked (to a core temperature of 70 °C [158 °F]) and that it be eaten before it cools.
Nine subjects ran at 70% VO2max in a hyperthermic environment (35°C, 70% relative humidity [RH]) until a core temperature of 39.5°C was reached, and for an equivalent time and intensity in the two remaining treatments.
Similar(4)
Accidental hypothermia concerns a body core temperature of less than 35 °C without a primary defect in the thermoregulatory system.
We recently described the transcriptomic and proteomic responses to heat injury and recovery in multiple organs in an in vivo model of conscious rats heated to a maximum core temperature of 41.8°C (Tc,Max).
Each was in deep coma with a measured core temperature of over 40 °C upon admission to the emergency department.
At a stellar core temperature of 18 Million Kelvin, the PP process and CNO cycle are equally efficient, and each type generates half of the star's net luminosity.
More suggestions(4)
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com