We studied thermal fluctuations in magnetoresistance (MR) signals originating from geometrically confined magnetic walls (GCMWs) of nanometer size. To this end, we developed a novel numerical simulation method which quantitatively evaluates the magnitude of thermal fluctuations in MR signals of magnetic nanostructures. Using the method, we first investigated the case when the twist angle Θ between the magnetization in a fixed layer and that in a free layer is 180°. We found that the thermal fluctuations of the magnetic structure of the 180° GCMW do not induce any crucial fluctuations in the MR signal because there is no significant difference among the MR values of the magnetic structures caused by the thermal fluctuations. We next investigated the dependence on the twist angle Θ of thermal fluctuations in MR signals. Since the GCMW is stabilized by decreasing Θ from 180°, the standard deviation (SD) of the MR signal is reduced with decreasing Θ. On the contrary, the SD/M ratio (M is the mean of the MR signal) monotonically increases with decreasing Θ because the attenuation of the mean value of MR is faster than that of the standard deviation. We also found that the SD/M ratio was not large for any of the temperatures (from 300 to 600 K) and twist angles (from 90° to 180°) we examined. The maximum value of the ratio, which was obtained when T = 600 K and Θ = 90°, was about 13%. This result indicates that thermal fluctuations do not cause significant noise in MR devices that utilize GCMWs of nanometer size.