News recommendation is often modeled as a sequential recommendation task, which assumes that there are rich short-term dependencies over historical clicked news. However, in news recommendation scenarios users usually have strong preferences on the temporal diversity of news information and may not tend to click similar news successively, which is very different from many sequential recommendation scenarios such as e-commerce recommendation. In this paper, we study whether news recommendation can be regarded as a standard sequential recommendation problem. Through extensive experiments on two real-world datasets, we find that modeling news recommendation as a sequential recommendation problem is suboptimal. To handle this challenge, we further propose a temporal diversity-aware news recommendation method that can promote candidate news that are diverse from recently clicked news, which can help predict future clicks more accurately. Experiments show that our approach can consistently improve various news recommendation methods.