In this study, we investigated the effect of a heat source on blood flow through a gradient-tapered vessel under the influence of a gradient magnetic field by reformulating the problem using a mathematical model representing the blood momentum and energy equations. The partial differential equations were dimensionlessly scaled using a scaling parameter and further reduced to a system of ordinary differential equations. A coupled system of regular equations was solved using the series method to obtain analytical solutions for temperature and blood velocity profiles. Numerical simulations were performed using Wolfram Mathematica version 12 and varied parameters relevant to the investigation. The results showed that the relevant parameters—magnetic field, radiation parameter, Grashof number, and tilt angle contributed to liquid temperature and blood flow velocity, respectively. The novelty of this study is the fact that heat can be introduced from a heat source for the purpose of helping blood circulation, and magnetic fields tend to accelerate blood flow velocity.