For nearly five years, the Heritage Foundation struggled with the question of how to build stronger ties with people who give between $1,000 and $10,000. Now, the organization thinks it has found the answer: outsourcing.

Since September, the Washington think tank has hired a telemarketing firm to provide three people to serve as representatives for its President’s Club.

Each representative is charged with building relationships with about 500 donors through personal phone calls and e-mail messages. Heritage plans to bring the representatives to its twice-yearly meetings for President’s Club members in Washington.

In the nine months since the effort started, the organization has learned about several bequests that supporters have created to benefit Heritage, and several other donors have increased their annual contributions to $10,000 or more.

“Anytime you pay attention in a...