Given a set of source data with pre-trained classification models, how can we fast and accurately select the most useful source data to improve the performance of a target task? We address the problem of measuring transferability for heterogeneous domains, where the source and the target data have different feature spaces and distributions. We propose Transmeter, a novel method to efficiently and accurately measure transferability of two datasets. Transmeter utilizes a pre-trained source classifier and a reconstruction loss to increase its efficiency and performance. Furthermore, Transmeter uses feature transformation layers, label-wise discriminators, and a mean distance loss to learn common representations for source and target domains. As a result, Transmeter and its variant give the most accurate performance in measuring transferability, while giving comparable running times compared to those of competitors.