Kate Hudson, A-Rod Bask in the Miami Heat

10/15/2009 at 04:15 PM EDT

Kate Hudson, A-Rod Bask in the Miami Heat
Alex Rodriguez and Kate Hudson (far right)
Juan Garces/Splash News Online

Kate Hudson

Kate Hudson

Temperatures rose for Kate Hudson and Alex Rodriguez as the lovebirds enjoyed some food and fun in steamy hot Miami this week.

On Monday, they were spotted lunching at Houstons in Coral Gables, one of the New York Yankees slugger's favorite informal eateries. He has been spotted there many times with this young daughters.

Afterward, they walked in and out of boutiques, including a beauty supply store in the romantic, old world section of Miami. "They looked happy and into what they were talking about," says a source who saw them together.

On Tuesday night, Hudson, 30, and Rodriguez, 34, sat in a private area behind a curtain at the popular, celeb-favorite steakhouse Prime 112, on South Beach.

"Kate and Alex definitely did not want to be seen while they had a cozy dinner," says a source. "They seemed really into each other."

Rodriguez – enjoying a great baseball season, maybe thanks to Kate – and the rest of the Yankees will play the Los Angeles Angels this weekend.

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