A new magnetorheological cell is implemented to perform measurements of temperature-controlled flows and determine viscoelastic properties in magnetic complex fluids under applied continuous magnetic fields. The flow properties of water-based and oil-based ferrofluids with volume fractions up to 10 % are investigated here in various situations of interparticle interaction, leading also to various microstructures already known from previous works. Shear flow behaviors under magnetic fields resulting in a competition between magnetic and hydrodynamic forces are directly related to the microscopic structure of the probed magnetic fluids.