Dengue, a mosquito-borne disease, poses a tremendous burden to human health with about 390 million annual dengue infections worldwide. The environmental temperature plays a major role in the mosquito life-cycle as well as the mosquito-human-mosquito dengue transmission cycle. While previous studies have provided useful insights into the understanding of dengue diseases, there is little emphasis put on the role of environmental temperature variation, especially diurnal variation, in the mosquito vector and dengue dynamics. In this study, we develop a mathematical model to investigate the impact of seasonal and diurnal temperature variations on the persistence of mosquito vector and dengue. Importantly, using a threshold dynamical system approach to our model, we formulate the mosquito reproduction number and the infection invasion threshold, which completely determine the global threshold dynamics of mosquito population and dengue transmission, respectively. Our model predicts that both seasonal and diurnal variations of the environmental temperature can be determinant factors for the persistence of mosquito vector and dengue. In general, our numerical estimates of the mosquito reproduction number and the infection invasion threshold show that places with higher diurnal or seasonal temperature variations have a tendency to suffer less from the burden of mosquito population and dengue epidemics. Our results provide novel insights into the theoretical understanding of the role of diurnal temperature, which can be beneficial for the control of mosquito vector and dengue spread.