We present a set of 3D global general relativistic radiation magnetohydrodynamic simulations of thin disks around non-rotating, stellar-mass black holes. We start from the standard Shakura-Sunyaev solution with an initial mass accretion rate of 0.03 LEdd/c2. Our previous work has confirmed that whenever such disks are supported by radiation pressure, they are thermally unstable. In the present work, we test the hypothesis that such disks can be stabilized by strong magnetic fields. We test three initial seed field configurations: 1) a zero-net-flux case with a single, radially extended set of magnetic field loops; 2) a zero-net-flux case with multiple, alternating sets of magnetic field loops; and 3) a net, vertical magnetic field configuration. Based on the results inferred from these simulations, we aim to address three key astrophysical questions: 1) What initial magnetic field configurations (if any) lead to a thermally stable accretion disk? 2) How does the thermally stable solution compare with the Shakura-Sunyaev one? and 3) What role do outflows play in these accretion disks? As these simulations include self-consistent radiative transfer, we can confront our findings with observed properties of black hole X-ray binaries.