The steady‐state temperature distribution within a block of cis‐polybutadiene has been mapped using quantitative magnetic resonance imaging. The experiment described makes use of the temperature dependence of the nuclear magnetic longitudinal relaxation time (T1) of the polymer protons. Hot and cold water flowed through two axially mounted pipes in a cylindrical sample, creating a dipolar temperature distribution. A fast inversion recovery imaging sequence was used to map T1 values in the sample with a spatial resolution of 0.3 mm and random error of ±5% for individual pixels in the 128×128 image. The T1 values thus obtained were converted into temperatures using an empirical calibration curve, leading to a temperature resolution of ±2 K for each pixel. Using a median filter (which reduces the image resolution by a variable factor of up to 3), the data are rendered smooth enough to obtain a clear contour plot. This is compared with a finite element solution of Laplace’s equation over the same domain, demonstrating that the MRI technique is reliable. A number of experimental problems limiting both the exact comparison between theory and experiment and the long‐term utility of the technique are discussed.