We present fiber optic sensors that utilize thin core fiber-multimode fiber-thin core fiber (TCF-MMF-TCF) structure for the simultaneous measurement of temperature and magnetic fields. The sensor features a silver (Ag) film coated on the TCF surface, and its design includes a fiber core offset sealed in a glass tube filled with magnetic fluid (MF) and a polydimethylsiloxane (PDMS) cavity. By integrating surface plasmon resonance (SPR) and Mach-Zehnder interference (MZI) into a single sensor, we have successfully addressed the issue of cross-sensitivity between magnetic fields and temperature, leading to improved measurement accuracy. Using the MZI principle, the sensor achieves a sensitivity of 21.97 pm/GS in the magnetic field range of 0-150 GS, and 94.06 pm/degrees C in the temperature range of 25 degrees C-80 degrees C. Additionally, using the SPR principle, the sensor exhibits a sensitivity of 0.217 nm/GS in the magnetic field range of 30-160 GS and -2.26 nm/degrees C in the temperature range of 0 degrees C-65 degrees C. Our experiments demonstrated that this sensor offers high sensitivity to both temperature and magnetic fields. In comparison to other sensors, it boasts small measurement error, high accuracy, high sensitivity, low cost, and a small sensing area. With the ability to achieve precise measurement and monitoring of temperature and magnetic field intensity, this sensor holds great potential for applications in biology, environmental monitoring, and beyond.