Attenuation of the unwanted heating of normal tissues due to eddy currents presents a major challenge in magnetic particle hyperthermia for cancer treatment. Eddy currents are a direct consequence of the applied alternating magnetic field, which is used to excite the nanoparticles in the tumor and have been shown to limit treatment efficacy in clinical trials. To overcome these challenges, this paper presents simple, clinically applicable, numerical approaches which reduce the temperature increase due to eddy currents in normal tissue and simultaneously retain magnetic nanoparticles heating efficiency within the tumor. More specifically, two protocols are examined which involve moving the heating source, an electromagnetic coil, relative to a tumor-bearing phantom tissue during the exposure. In the first protocol, the linear motion of the coil on one side with respect to the hypothesized tumor location inside the phantom is simulated. The estimated maximum temperature increase in the healthy tissue and tumor is reduced by 12% and 9%, respectively, compared to a non-moving coil, which is the control protocol. The second technique involves a symmetrical variation of the first one, where the coil is moving left and right of the phantom in a bidirectional fashion. This protocol is considered as the optimum one, since the estimated maximum temperature rise of the healthy tissue and tumor is reduced by 25% and 1%, respectively, compared to the control protocol. Thus, the advantages of a linearly moving coil are assessed through tissue sparing, rendering this technique suitable for magnetic particle hyperthermia treatment.