The climate may not be warming as much as the increase of temperatures recorded in cities appears to suggest.

as从句省略了to suggest的宾语从句that it will be. 补全的从句为：

as the increase of temperatures recorded in cities主语 appears to suggest复合谓语 that it will (be)宾语从句.

it指代the climate. suggest的宾语从句与主句结构相同故可省略。