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In paparazzi pictures, Renée Zellweger and Bradley Cooper seem to generate all the heat of an Easy-Bake Oven. But behind the scenes, their flame is apparently burning hot and heavy.

Following a bout of quantity bonding time with the actor's family over the holidays and a quick trip this week to the Sundance Film Festival, the private pair of six-plus months is reportedly looking to get settled in Cooper's new $4.7 million digs in Pacific Palisades, Calif.

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They were snapped checking out the under-renovation three-bedroom, three-bath house on Tuesday, with the gym-toned Oscar winner hiding inside an ensemble best described as Unabomber chic.

According to People magazine, Renée, who has already made herself at home in Bradley's Venice, Calif., abode, loves his spacious new pad and intends to stay there when she's in town (she has a swanky Manhattan apartment, along with homes in Connecticut and the Hamptons).

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She just needs to keep an eye out for the neighbors. TMZ reports she had a close call outside the house on Thursday morning when a BMW sideswiped her Prius as she was climbing in.

Thankfully, there were no injuries, except to her enviro-friendly vehicle, and Coop, considerate guy that he is, arrived soon after the accident (her latest) and picked her up.

Not surprisingly, the casual cohabitation talk has led to another round of engagement speculation.

"Bradley has fast-tracked the romance and he's ready to get married," a mole alleges to In Touch, which is convinced a vow-swap will take place "sooner than later."

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The source claims Cooper "already has a setting he likes," and he supposedly went on a rock recon mission during a recent stay in New York. Oh, and he "wore a hat and dark glasses" in order to remain under-the-radar during his diamond shopping.

"He is old-fashioned," says the snitch. "He'll probably get down on one knee and propose in a romantic setting -- and I wouldn't be surprised if it was on Valentine's Day."

That date would have Cooper's management team doing a happy dance given that it's also the title of his soon-to-be-released, star-laden rom-com. Nothing like a little synergy with one's personal and professional lives.

If Renée and Bradley are considering tying the knot (and that's an "if" bigger than Bridget Jones' underpants), it shows considerable optimism on both their parts.

Neither had much luck with their first trip to the altar: She annulled her four-month union to country crooner Kenny Chesney in 2005, while his December 2006 marriage to actress Jennifer Esposito also fizzled out after four months.

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