They may get too hot and have to spend more time trying to escape from the sun中 trying to escape from the sun是非谓语动词作状语修饰谓语动词spend吗,所以是方式状语吗。trying to escape from the sun逻辑主语是they对吧。
据我了解,对spend time+doing结构目前主要有两种认识:1.v-ing是现在分词,作方式状语;2.v-ing是动名词,其前省略了介词in(这种省略在口语中更为常见,其中in+v-ing作方面状语)。
如果按照现在分词短语作状语来看待,trying to escape from the sun的逻辑主语应为句子的主语they。