NEW YORK (CNNMoney.com) - With the average price of gas hovering at just under $3 a gallon nationwide, will Americans cut back on going to theme parks this summer?

It's an important question for Walt Disney (Research), which will report its fiscal second-quarter results on Tuesday. Theme parks account for more than a quarter of the company's sales and operating profits.

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A recovery in attendance at Disney's parks and resorts is one reason why Disney's stock is the best-performing media stock this year. Shares are up 21 percent.

Lowell Singer, an analyst with Cowen & Co., wrote in a report Monday that the strong attendance growth has led to better than expected profit margins for the parks and resorts business for the past two quarters.

But it will be interesting to see if attendance was hurt during the quarter that ended in March. More importantly, what will management say about expectations for the fiscal third-quarter, which ends in June?

Few energy analysts expect gas prices to come down substantially anytime soon and that could eat into consumers' discretionary spending budgets.

Still, Disney does not appear to be concerned about rising gas prices.

"Historically, Disney's theme parks and resorts nave not been noticeably impacted by rising gas prices," said Lisa Haines, a spokesperson for Walt Disney Parks & Resorts. "Vacations are one of the last things people will cut."

But another theme park operator, Cedar Fair (Research), which operates seven amusement parks and five water parks in the U.S., has already announced that is cutting prices in response to rising energy costs.

"In 2006 we know that many of our guests will be feeling the pressure of increased prices at the gas pump," said Dick Kinzel, chairman and chief executive officer of Cedar Fun, during a conference call discussing the company's first quarter results last week.

Six Flags (Research) is also taking steps to make sure customers don't stay home because of high gas prices. The company announced on Friday a $15 discount for up to six admission tickets to any of its 13 parks to consumers showing up with a receipt for a recent gas purchase. The offer is valid until May 29.

"We've seen what's going on with gas prices and we understand the dilemma the American consumer is facing," said Mark Shapiro, president and CEO of Six Flags in a statement. The company will report its first quarter results after the closing bell Monday.

Disney, though, should be less affected by rising gas prices in the near-term since a trip to its resorts typically involves making reservations months in advance. Many of its attendees fly, as opposed to drive, to the company's Walt Disney World resort in Orlando, Fla. for an extended vacation instead of just visiting for a day.

"There's a lagging effect. Most people who are going to Disney in Florida have already made their summer plans and have reservations. In the short-term there's not much people can do to change that," said Dennis McAlpine, an independent media analyst who follows Disney.

Alan Gould, an analyst with Natexis Bleichroeder, added that so far, gas prices shouldn't pose a major problem for Disney. He said that historically, people only have cut back sizably on driving when there are gas shortages. And the current price spike in oil and gas is being fueled (pardon the pun) by strong demand, not supply shortages like there was in the 1970s.

"Not that the price of gas at $3 a gallon helps but availability of gas has typically been much more important than the price," he said.

But McAlpine said that if gas prices remain high, attendance could be hurt at Disneyland in Anaheim, Calif. this summer since he estimates that about 30 percent of that park's visitors are locals who drive to the park.

In addition, if oil and gas prices continue to remain high, it could cause consumers to pull back on booking trips later this year.

Another issue: Since last May, Disney has run special promotions in all its parks worldwide to celebrate last year's 50th anniversary of the opening of Disneyland. These promotions are scheduled to end in November.

Singer wrote that it is "unclear whether recent momentum in attendance growth will continue" after the promotions end. He added that "worse-than-expected parks & resorts results due to higher fuel prices that lead to an increase in airline fares," is one of the risks for Disney investors.

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For trips on how to cut your summer travel costs, click here.

For more about the outlook for Disney and other big media companies, click here.

A member of Cowen's research team covering Disney has a long position in the stock but the firm has no banking relationship with the company. McAlpine and Gould do not own the stock and their firms have not done investment banking for the company.