In order to meet rapid changes of Web information, it is necessary to extend the current Web technologies to represent both the valid time and location of each fact and knowledge, and reason their relationships. Until recently, many researches on qualitative temporal reasoning have been conducted in laboratory-scale, dealing with small knowledge bases. However, in this paper, we propose the design and implementation of a parallel qualitative temporal reasoner, MRQUTER, which can make reasoning over Web-scale large knowledge bases. This parallel temporal reasoner was built on a Hadoop cluster system using the MapReduce parallel programming framework. It decomposes the entire qualitative temporal reasoning process into several MapReduce jobs such as the encoding and decoding job, the inverse and equal reasoning job, the transitive reasoning job, the refining job, and applies some optimization techniques into each component reasoning job implemented with a pair of Map and Reduce functions. Through experiments using large benchmarking temporal knowledge bases, MRQUTER shows high reasoning performance and scalability.