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The magnetic hyperfine field is smaller at higher temperatures. This is clear from the pictures shown in the video: The lower the T, the more influence you see from the magnetic field.
The magnetic moments tend to align themselves for a minimal energy configuration. In this minimal energy configuration, all moments add up and the magnetic hyperfine field becomes maximal. This effect is counteracted by thermal agitation, which tries to randomize all magnetic moments. At high T, this effect takes the upper hand and there is no magnetic hyperfine field. At lower T, the alignment wins from the thermal agitation and a magnetic hyperfine field arises.
Correction: the orientation of the magnetic moments has nothing to do with the strength of the magnetic hyperfine field. This field arises due to the presence of electrons around (or inside) the atomic nucleus. This does not change with temperature, so the magnetic hyperfine field will be the same for all temperatures.
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