The Hannukah festivities at the Museum of Jewish Heritage may burn hotter than normal today. Mayor Bloomberg is to host a holiday event at the venue — of which his rival, DA Robert Morgenthau, is board chairman, and the two could cross paths. A source said the strain goes back to when City Hall dropped the ball on a charity dinner for the museum. In April, 2004, Morgy bumped into Bloomberg at an event and asked him to be the honoree. Bloomberg agreed on the spot, but his staff apparently didn’t get the message. When the museum used his name to publicize the event, Deputy Mayor Patti Harris put the kibosh on his award-getting, and Bloomberg attended as a guest. A mayoral rep said he “attended at the DA’s request and was glad to go.”