•The magnetic fluid heat transfer in biological over a semi-infinite region is investigated.•Absorbing boundary condition is deduced by artificial boundary method.•The superiority of the absorbing boundary condition is discussed.•Important parameters of biological heat transfer and magnetohydrodynamic properties are analyzed. This paper introduces modifications to the classical Pennes’ equation through the Cattaneo correction and considers the influence of a magnetic field on the heat generation of the fluid in a semi-infinite region. The traditional method to treat the problem in unbounded regions is to use a large interval to approximate the infinite region, which leads to large deviations of the solution at the truncated boundaries for a long-time numerical simulation. Using the artificial boundary method, the problem in infinite domains can be converted into an equivalent problem in the bounded domains with the absorbing boundary condition, of which the solution would be more physically reasonable and accurate. The governing equation subject to the absorbing boundary condition is discretized using the finite difference method and leads to effective numerical solutions. We analyze the effects of various parameters including the relaxation parameter, heat transfer coefficient, blood perfusion rate, blood tissue density, magnetic fluid concentration, magnitude, magnetic field frequency, and oscillatory boundary condition on the temperature distribution. The study validates the effectiveness of the absorbing boundary condition when addressing problems in unbounded regions. Some important findings are that the relaxation parameter has a delay effect on magnetic fluid heat transfer and magnetic fluid concentration, and the magnetic field strength and magnetic field frequency are directly proportional to magnetic fluid heat production.