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The phrase "a uniform temperature" is correct and usable in written English
You can use it when you need to refer to a temperature that is consistent across a certain area or environment. For example, "The air conditioning system ensures a uniform temperature throughout the building."
Exact(60)
Achieving a uniform temperature in the 39-story building, which was built in 1952, ranks up there with world peace as a noble, if unlikely, goal.
One of my jobs was working at a local steelworks plant, heating iron ingots to a uniform temperature, which could be as much as 1,300 degrees.
After it has cooled and has reached the same density as the water below, the water column becomes isothermal (i.e., there is a uniform temperature at all depths).
In most continuous casting operations, it is necessary to maintain minimal fluctuation in steel temperature, and this requires the use of a ladle stirring station to establish a uniform temperature and chemical composition throughout the ladle.
In physics terms, there's a "uniform temperature gradient".
During thermal cycling, the solder layer reaches a uniform temperature.
The second assumption of a uniform temperature of 25°C also needs to be examined.
A uniform temperature distribution is obtained in this type of gasifiers.
A uniform temperature along the length of the channel is assumed.
A temperature control system was also developed to establish a uniform temperature inside the powder sample.
It is assumed that the wavy surface is electrically insulated and is maintained at a uniform temperature T w.
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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