Kitchens with no air conditioning reach more than 60C (140F), Tory defence spokesman Lord Astor said.
He said it was so hot, computers were continually breaking down.
Junior defence minister Lord Drayson said air conditioning was gradually being installed, but said the MoD had not had complaints from kitchen staff.
Lord Astor asked: "Why are detainers in the Intelligence Corps still interrogating suspects in rooms without air conditioning?
"Computers are continually breaking down because of the heat and losing vital information.
"And why, after three years, are cooks and kitchen staff still working in temperatures in excess of 60C, that is 140F, and it's totally unacceptable."
In response Lord Drayson said that three camps with 500 troops were in line for air conditioning, and it had already been installed at Basra Palace.
There were 68 stand-alone units in two camps and the Shatt al Arab hotel, which is occupied by British troops.
Lord Drayson added that all fixed living accommodation would have air conditioning by next year's hot season.
He added that only a "small proportion" of tents were not yet air conditioned.
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