The site (www.wewantwade.com) crashed within hours of the Heat's announcement of its creation and technicians were moving it to new servers to accommodate the interest, the Heat's chief marketing officer, Michael McCullough, told Reuters.
Wade, a Chicago native and the fifth overall pick in the 2003 NBA Draft, can become a free agent this summer and leave Miami, his basketball home for the last seven years.
The "We Want Wade" website is part of a multifaceted full-court press to keep the popular 28-year-old guard in a Heat uniform.
Fans can send messages and videos, call a special hotline, check out billboards throughout the region and perhaps see their communities rename streets to honor the talented guard.
"We wanted to let him know the people in south Florida love him and want him to stay right here," McCullough said in a telephone interview.
There is also a kit available that includes instructions on what to do if one encounters Wade.
"If you happen to be at the same restaurant he is at, it's OK to give him a brief standing ovation or send a dessert to his table, that's very classy," said McCullough.
"What you don't want to do is ask him for an autograph, one of his cars or a date."
Wade appeared to enjoy the website.
"I didn't expect anything like that," he told reporters. "I thought it was hilarious. But I appreciate it. I do, I really do."
(Writing by Gene Cherry in Raleigh; Editing by Steve Ginsburg)