Hi Alan. Sorry this comment languished in the inbox for so long.  Here are some quick responses: 

Doesn’t increase rainfall actually (in the long run) decrease air temperature? 

It sounds like you're asking whether this increased heavy rainfall will somehow reverse the warming due to greenhouse gas increases. The answer to that is no. The process of evaporation and rainfall can only move heat energy from one part of the atmosphere to another. It takes energy to evaporate water from the surface, and that latent heat is carried by the water vapor molecules up into the higher, colder parts of the atmosphere. Eventually, it reaches a place where the ambient air is too cold for water vapor to remain in a gas state. As the water vapor condenses into liquid water or freezes into ice crystals, it releases that latent heat energy that evaporated it back into the atmosphere. The process cools the surface, but it warms the atmosphere where it rains. Heat energy is recycled, but not removed from the system. 

How do we know if this is a unique event without knowing temperature and humidity data from other more distant historical time periods?

I'm not totally sure what you are referring to when you say "a unique event." This post is about a long-term trend in heavy rain. So, the point of the post was not that the amount of heavy rain we receive today is unique in all of Earth history. The point was that the heaviest rainfall events we experience today are bigger than the heaviest rain events that occurred a hundred years ago. This is significant because our modern infrastructure and ag systems are designed to handle the old climate, not the new one.   

How do we know if we aren’t still coming out of the ice age, or going back in to another ice age?

I recommend this peer-reviewed scientific paper that addresses that very question.