Densification through small cells and caching in base stations have been proposed to deal with the increasing demand for Internet content and the related overload on the cellular infrastructure. However, these solutions are expensive to install and maintain. Instead, using vehicles acting as mobile caches might represent an interesting alternative. In our work, we assume that users can query nearby vehicles for some time, and be redirected to the cellular infrastructure when the deadline expires. Beyond reducing costs, in such an architecture, through vehicle mobility, a user sees a much larger variety of locally accessible content within only few minutes. Unlike most of the related works on delay tolerant access, we consider the impact on the user experience by assigning different retrieval deadlines per content. In our paper, we provide the following contributions: (i) we model analytically such a scenario; (ii) we formulate an optimization problem to maximize the traffic offloaded while ensuring user experience guarantees; (iii) we propose a variable deadline policy; (iv) we perform realistic trace-based simulations, and we show that, even with low technology penetration rate, more than 60% of the total traffic can be offloaded which is around 20% larger compared to existing allocation policies.