Many refined oils from soybean, rapeseed, and sunflower, among others, are available on the food market, except olive oil. Refining, on the small production scale of niche oils, is not used due to the high cost of the refining process. Unrefined oils are characterized by intense taste, odor, color, and undesirable nutrients. The problem to be solved is determining the effects of incomplete refining of niche oils on their composition. One process, which does not require the use of complex apparatus, is the bleaching process. The results presented in this article relate to the research stage, in which the aim is to evaluate the changes occurring in the oil due to the low-temperature bleaching process with different process parameters. The presented research results provide evidence of the absence of adverse changes in the fatty acid profile of hemp oil of the varieties ‘Finola’, ‘Earlina 8FC’, and ‘Secuieni Jubileu’. Seven different types of bleaching earth were used to bleach the oil in amounts of 2.5 and 5 g/100 g of vegetable oil. The fatty acid profile was obtained by gas chromatography (GC-FID). The obtained chromatograms were subjected to statistical analysis and principal component analysis (PCA). The results show that there was no effect of the type of bleaching earth and its amount on the change in the fatty acid profile of bleached oils. Only real differences between the types of hemp oils were observed. However, an overall positive effect of the bleaching process on hemp oil was found. The amount of saturated fatty acid (SFA) was reduced by 17.1% compared with the initial value, resulting in an increase in the proportion of polyunsaturated fatty acids (PUFA) by 4.4%, resulting in an unsaturated fatty acid (UFA) proportion of 90%. There was a significant improvement in the SFA/PUFA ratio by 26% over the baseline, and the omega-6/omega-3 ratio by 8.9% to a value of 3.1:1. The new knowledge from this study is evidence of the positive effect of the low-temperature bleaching process on the fatty acid profile. In contrast, the parameters of the bleaching process itself are not significant.