WASHINGTON (Reuters) - With a smile periodically playing across his face, Ben Bernanke almost looked pleased to face questions from members of the House of Representatives on Wednesday, but that might be because he knows that it was for the last time.

During a hearing described several times as more like a eulogy than testimony on monetary policy, the Federal Reserve chief received bi-partisan thanks for his service as successive members said they had heard he may not be in the job next year.

Bernanke has kept silent about his future plans, but he is widely expected to depart when his current term as Fed chairman expires on January 31. Nor has he pushed back against perceptions that he is ready to return to private life.

That impression was reinforced last month by President Barack Obama, who said Bernanke had already stayed in office "a lot longer than he wanted."

"I feel a little bit like Bette Midler, the very last guest on the very last episode of The Tonight Show that Johnny Carson hosted. She famously quipped to Mr. Carson, 'You are the wind beneath my wings," said Washington state Democrat Denny Heck.

"There's some application to that ... as it relates to the economy and I thank you for your service," he said.

Another Democrat, Al Green from Texas, pleaded with him not to go, while it was suggested that T-shirts for his retirement party be printed with the logo "$34 trillion" to celebrate the amount of U.S. household wealth restored on his watch.

Democrats have been staunch supporters of Bernanke, even though he is a Republican originally appointed by President George W. Bush. Obama tapped the one-time Princeton professor for a second four-year term in 2009, thanking him for his aggressive efforts to combat the deep 2007-09 recession and virulent financial crisis.

The Bernanke-led Fed cut overnight interest rates to near zero in late 2008 and launched an unconventional policy of buying longer-term government and mortgage-backed debt to drive other borrowing costs lower.

Many Republicans privately blame Bernanke for helping Obama get re-elected in 2012 and have been outspoken public critics of the aggressive policies he has championed.

Some Republicans repeated their complaints on Wednesday, but they also spent time warmly acknowledging his service, while noting this could be his last appearance before the House.

Indeed, the atmosphere in the crowded hearing room was a great deal lighter than during the dark days of the financial crisis when Bernanke had to endure a heavy barrage of critiques, and the Fed chief looked more at ease.

One lawmaker asked him if now would be a good time for a friend to refinance his mortgage. Bernanke cheerfully responded: "I am not a qualified financial adviser."

However, there were moments when he looked as if he might be relieved he would not have to endure long-winded congressional hearings for much longer, although he does address the Senate banking panel on Thursday.

His smile thinned when committee Chairman Jeb Hensarling, a Texas Republican, announced three hours into the hearing that Bernanke would have to sit through another 10 minutes of questioning.

And he slumped visibly, head on hand, as he listened to Michele Bachmann, a Republican from Minnesota, wonder aloud whether the U.S. Treasury was cooking the books on the federal budget, before politely deflecting her question.

Likewise, his final words to the committee, in response to a question from New Mexico Republican Steve Pearce about whether there was a level of immigration into the United States that could hurt the economy, sounded unapologetically dismissive: "I don't know."

(Additional reporting by Paige Gance; Editing by Chizu Nomiyama)

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