A Kansas City Star article from 1997 identified the voice as that of a WAGA-TV Atlanta meteorologist, John Doyle. The equipment for the service was provided by Audichron USA, also of Atlanta. Time and temperature were both given. The recordings of Doyle's voice were digitized and sent "by modem" to Kansas City. The system kept time internally. The Star article said the service received more than 100-thousand calls a day.
Edit: I found another Star article, this one from 2002, indicating that the service would be shut down November 18 of that year. It stated that the time was synchronized to a NIST atomic clock in Boulder, Colorado (I believe this should have referred to Fort Collins). It had been in service for 53 years at that point and was still getting 70-thousand calls a day. The equipment, apparently the same equipment as described in the 1997 article, was described as obsolete and costly to upgrade.