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The hysteretic, nonlinear character of ferromagnetic steels, coupled with pronounced stress and temperature sensitivities, make detailed magnetoelastic sensor design and calibration very difficult at present, particularly under possible high repetition rates during disaster scenarios, and in large cables (δ/R<1,Bi<0.1, where δ is the magnetic skin depth and Bi is the thermal Biot number) with inhomogeneous stress and thermal fields. The desire also exists to associate bulk magnetic material parameters with microstructural features to enable generally useful correlations to be developed. The Jiles-Atherton class of thermodynamic models potentially fit these requirements, and we explore their use for investigating field thermomagnetic effects in A36/1018 steels. Model development is supported by microstructural characterization of the anhysteretic via magnetic force microscopy and tunneling electron microscope imaging.