In order to meet the required power and energy demand of battery-powered applications, battery packs are constructed from a multitude of battery cells. For safety and control purposes, an accurate estimate of the temperature of each battery cell is of vital importance. Using electrochemical impedance spectroscopy (EIS), the battery temperature can be inferred from the impedance. However, performing EIS measurements simultaneously at the same frequency on each cell in a battery pack introduces crosstalk interference in surrounding cells, which may cause EIS measurements in battery packs to be inaccurate. Also, currents flowing through the pack interfere with impedance measurements on the cell level. In this paper, we propose, analyse, and validate a method for estimating the battery temperature in a battery pack in the presence of these disturbances. First, we extend an existing and effective estimation framework for impedance-based temperature estimation towards estimating the temperature of each cell in a pack in the presence of crosstalk and (dis)charge currents. Second, the proposed method is analysed and validated on a two-cell battery pack, which is the first step towards development of this method for a full-size battery pack. Monte Carlo simulations are used to find suitable measurement settings that yield small estimation errors and it is demonstrated experimentally that, over a range of temperatures, the method yields an accuracy of +/- 1 degrees C in terms of bias, in the presence of both disturbances.