Channel bandwidth available for a message on a communication network varies with time and link. This variation (heterogeneity) can have a significant effect on performance of an individual message and also that of the network as a whole. Therefore, it is necessary to understand effects of bandwidth heterogeneity on the network performance in order to optimally utilize a heterogeneous communication network. The ability to use such a network optimally is highly desirable in many applications such as network-based data-intensive high performance computing. The main goal of this study, as the first step toward developing effective schemes to utilize heterogeneous communication networks, is to analyze effects of temporal and spatial heterogeneity on performance of individual messages in detail via an extensive simulation, in terms of throughput, end-to-end delay, etc. Also, the problems of path selection and multi-path data transfer are considered to illustrate how the analysis results may be used in the future effort of optimizing the network performance by taking channel bandwidth heterogeneity into account.