The efficiency of power transformers should be always taken in account when design and operation conditions parameters are chosen. In high temperature superconducting transformers (HTS transformers), normally cooled by liquid nitrogen at 77 K, cores are usually kept at room temperature in order to minimize total magnetic losses, losing the possibility to use the cooling liquid to minimize electric risks and to cool the core, and increasing the complexity of the cryostats that, in these cases, must only embrace the superconducting windings. This work try to evaluate the magnetic core losses increasing at 77 K, for different magnetic materials, and the possibility of reducing these losses under some specific manipulation of magnetic materials. For this purpose, several low temperature measurements are presented to characterize the magnetic behavior of four electrical steels usually used in transformer cores. The chosen magnetic materials are three crystalline materials, two grain-oriented and one non oriented steel, and an amorphous elaectrical steel. The most significant results show that grain oriented steels have lower losses increasing at cryogenic temperature, comparing with the other two magnetic materials, and that above a certain value of magnetic induction, B, total magnetic losses at 77 K became smaller than room temperature losses. Results interpretation is presented and some suggestions are made concerning production of magnetic materials for applications at 77 K.