Blazer said last week that while Bin Hammam's Qatar can air-condition its stadiums, "I don't see how you can air-condition an entire country."
Blazer's comments were backed by FIFA's technical report, which said that taking the tournament to Qatar for the first time would be a "potential health risk" because of the heat. Average temperatures during the tournament would be 106 degrees.
But Bin Hammam of Qatar has pointed out to Blazer that extreme temperatures are also an issue in parts of the United States, which hosted the tournament in 1994.
"When my counterpart asked me about my response to the news that my country's bid was once more criticized due to Qatar's hot weather and the danger it may contribute toward players' and officials' health, I reminded him of two things," Bin Hammam wrote on his website.
"One: the technological developments and solutions that Qatar would apply to its stadiums in order to overcome the challenges of the heat. Two: whether or not he remembers the 1994 World Cup in the United States, where some of the matches were played at midday in temperatures as high as 50 degrees Celsius (122 degrees Fahrenheit)."
Bin Hammam claimed that "American fans forgot about the heat, and yet, (organizers) applied for another World Cup posting in less than 16 years from the time they last hosted."
The American bid received a possible boost last weekend from Major League Soccer, which announced it will consider aligning its schedule with soccer's international calendar, responding to criticism from FIFA president Sepp Blatter.
Blatter has said the current March-November season is the overwhelming reason the MLS cannot compete with top leagues in Europe. Aligning with the international calendar would help MLS teams attract top talent — and avoid losing players to national team duty for World Cup qualifiers.
"We're going to do a study, we're going to take the time to get it right," MLS Commissioner Don Garber said.
Qatar and the U.S. are competing with Australia, Japan and South Korea for the right to host the 2022 tournament.
Bin Hammam, Blazer and Blatter are on the FIFA executive committee that will vote on the 2018 and 2022 hosts in Zurich on Dec. 2.
The number of voters was reduced to 22 when Nigeria's Amos Adamu and Tahiti's Reynald Temarii were suspended last week for ethics violations over an undercover investigation by The Sunday Times of London.
FIFA's ethics committee banned Adamu from all soccer activity for three years for allegedly agreeing to take bribes from the undercover reporters who posed as lobbyists trying to buy votes.
Temarii, the president of the Oceania confederation, received a one-year ban for breaching FIFA's loyalty and confidentiality rules when he was secretly filmed.
On Monday, FIFA vice president Chung Mong-joon said it was obvious the two members' remarks were "not careful," but he questioned if their behavior was serious enough to warrant such a punishment.
"I personally believe the disciplinary measures on the two executive committee members are excessive," Chung told reporters in Seoul.
He said many other executive members have also expressed regret over the suspension.