This paper presents Time Series Multi-Task Question Answering (Time-MQA), an integrated framework for diverse temporal time series data (e.g., finance, healthcare, energy, etc.). Time-MQA supports natural language questions that enable open-ended question answering, including numerical analysis tasks and inference. At its core is a large-scale dataset, TSQA, containing approximately 200,000 question-answer pairs derived from diverse temporal time series data (e.g., environment, transportation, etc.). TSQA handles temporal time series of various lengths and facilitates the development of robust models. In addition, we demonstrate that large-scale language models, such as Mistral 7B, Llama-3 8B, and Qwen-2.5 7B, can be pre-trained on the TSQA dataset to enhance temporal time series inference capabilities and enable more sophisticated and intuitive interactions with temporal data beyond simple numerical tasks. The TSQA dataset, models, user study questionnaires for evaluation, and other related materials are open-sourced.