Educate.

Names and contact details are great assets, and cold-calling as you say can be effective.

Now diversify your efforts. Cold-calling is about sales, it is a direct fairly yes/no conversation.
At the same time use other channels to educate your audience. What is happening in your industry that can impact your clients? What are alternatives to their problems they may not have considered? What news should they be aware of?
Use content to engage in a different way and start on-going conversations, in addition to the yes/no ones.