Raman distributed temperature sensing (RDTS) obtains the temperature information by measuring the intensities of Raman scattering lights. The anti-stokes only RDTS can avoid the error caused by wavelength-dependent loss and dispersion. However, to eliminate temperature-independent intensity variations, single-wavelength demodulation generally adopts the double-ended detection scheme. This requires two optical fibers or one fiber to be folded into a loop, which is inconvenient in practical applications. Moreover, the temperature accuracy of such a scheme is lower than the conventional single-ended system, so it has not been widely used. Here, we propose and experimentally demonstrate a multi-core fiber (MCF) based RDTS system. A single-ended loop structure is achieved by connecting two cores at the far end of the MCF with a fan-in/fan-out device. By measuring the backscattered anti-stokes lights in the two cores, the results can be self-calibrated to eliminate the influence of temperature-independent light intensity changes. Besides, the results can be improved by averaging the temperatures of the two cores due to the spatial consistency of the MCF. Moreover, to further improve the temperature uncertainty, we employ the one-dimensional denoising convolutional neural network. Finally, a maximum temperature uncertainty of 1.4 °C is achieved over a 10 km MCF with a 3 m spatial resolution.