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"at a higher temperature" is a correct and usable phrase in written English.
You can use it to refer to a physical object or environment that is being heated up to a higher than usual temperature. For example: "He turned up the oven, and the cookies began to bake at a higher temperature."
Exact(60)
The end result is that you can make snow at a higher temperature".
Those smelting mills needed charcoal, which burns at a higher temperature than well-seasoned wood.
High-test butter melts slowly in a saucepan and burns at a higher temperature.
Diamond's higher bandgap means it shorts out at a higher temperature.
The "new iPad" – AKA iPad 3 – operates at a higher temperature than its predecessor, according to tests.
(But it can also be cooked more quickly at a higher temperature).
The skin is roasted at a higher temperature until it's crisp.
On cooling, one molecule assembles at a higher temperature than the other, which can result in a self-sorted network.
Annealing is faster at elevated temperatures; also, damage is less when the irradiation is at a higher temperature.
Hence, a second crossover at which superfluidity disappears when vortex pairs unbind must be expected at a higher temperature, T̃BKT.
Finding a superconductor that operates at a higher temperature, for applied use, is a holy grail of condensed matter physics.
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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