Temporality and uncertainty are important features of many real world systems. Solving problems in such systems requires the use of formal mechanism such as logic systems, statistical methods or other reasoning and decision-making methods. In this paper, we propose a linguistic truth-valued temporal reasoning formalism to enable the management of both features concurrently using a linguistic truth valued logic and a temporal logic. We also provide a backward reasoning algorithm which allows the answering of user queries. A simple but realistic scenario in a smart home application is used to illustrate our work.