Open the sender settings for any of your accounts and copy your Warmup Identifier Tag

 

Create a new folder/label called "Warmup" in your mail account with your ESP.

 

Create a filter for any email that hits your inbox AND contains the Warmup Identifier Tag in the body to be marked as read and move to archive.

 

Gmail Filter Example

  1. Create a folder called "Warmup" 
  2. Create a filter:

 
"Includes the words" is where you put your Warmup Identifier Tag.
 
 
Click "Create filter" for the settings to open. Then check the marked checkbox and click "Create a filter"