Heymarket allows searching through the message and contact history in chats. You can search for a specific name, word, or phrase.
The search is designed to look in the inbox and filter you are currently in, so if you want to search for a specific message to a contact that you've closed, switch to Closed. In the example below, you can see searching for the word order in Closed returned two results.
You can also search for specific names -- for example, searching for Crissie in the inbox returned the contact for Crissie as well as messages with the word Crissie in them.
This search feature is currently available for only the web version of Heymarket.