Klempner grew up in New York City, and attended Cornell University, graduating Phi Beta Kappa in 1997, and winning a J. William Fulbright Fellowship. In 2000, he received an M.A. in folklore from the University of North Carolina at Chapel Hill.

Klempner spent nearly a decade talking with and getting to know Dutch "Righteous Among the Nations" in order to write The Heart Has Reasons: Holocaust Rescuers and Their Stories of Courage, Cleveland: The Pilgrim Press, 2006. He found the rescuers through Yad Vashem, and was originally funded by a research grant from the Institute for European Studies at Cornell University. Most of the rescuers he interviewed were previously unknown to the general public, with the exception of Miep Gies, who tried to save Anne Frank and her family. Because Klempner is the son of a Jewish immigrant who barely escaped the Holocaust, he found that his subjects sometimes looked at him as the child or grandchild of the Jews they rescued. He later conducted archival research at The United States Holocaust Memorial Museum and The Netherlands Institute for War Documentation. The published book contains a foreword by renowned Holocaust historian Christopher Browning.

Klempner's articles on oral history methodology have appeared internationally in professional journals and anthologies such as The Oral History Reader. He has also been a guest columnist for mainstream periodicals such as the Christian Science Monitor and the Baltimore Sun as well as progressive religious periodicals like the National Catholic Reporter and Tikkun. His op-eds often tackle difficult political and social issues, such as his piece "The Internet: Our Last Hope for a Free Press," which has received more than 1,000 Diggs. He has also been featured as a radio commentator on Morning Edition, and has been interviewed on Air America Radio, NPR, Prime Time Radio and other broadcast media in the United States. His work has appeared on the internet at such sites as Common Dreams, Alternet, The Huffington Post, The Social Edge and Sojo Mail, the weekly newsletter of Jim Wallis' Sojourners community.