Huckabee, a former Arkansas governor, finished second in this month's Iowa straw poll but lags nationally among his rivals in fundraising and public support. Thompson, an actor and former Tennessee governor, has polled well in the crowded field despite his unofficial status.
"Let's just hope Fred decides it's just too hot this summer to even do this. Maybe he won't get in," Huckabee said in a broadcast interview Sunday.
"But if he does, I think he's going to suck a lot of the oxygen out of the room when he first comes in. But I'm not sure I'd want to be in his position where the expectations are simply just sky-high for him to be able to perform," Huckabee said.
Thompson, in a speech Saturday night at the Midwest Republican Leadership Conference in Indianapolis, said he was in a sound position to seek the nomination even though others in the race announced their candidacies long ago.
"We have done within a few months what other people have spent much longer periods of time doing," Thompson told reporters. He is expected to announce his bid early in September.
Huckabee said he would rather "be in a position to overperform than to get in and then underperform the expectations. And so far, that's what we've done," citing the results in Iowa and saying he has gained momentum in New Hampshire.
Referring to Thompson, Huckabee said, "People are expecting him to basically come in and be the fifth head on Mount Rushmore. Whether he can live up to that -- I think there's a real challenge for anybody to live up to that, including if Ronald Reagan were to come back. I'm not sure he could live up to Ronald Reagan's persona and image at this stage."
Huckabee spoke on "Fox News Sunday."