Thank You for Sending Me an Angel first appeared on Talking Heads' second album More Songs About Buildings and Food in 1978
Here's a splendid live version from that year
Luna's cover was first released on their Bonnie and Clyde single on Beggars Banquet in 1995 and later on their EP on No.6.
Here's a live version from San Francisco in February 1994
MP3: Luna - Thank You for Sending Me an Angel (live in San Francisco, Februaru 1994)