In a method for fabricating a brazed aluminum fin heat exchanger comprising a pair of brazing sheets each consisting of a core sheet and a cladding of brazing material disposed on either side of said core sheet and a corrugated fin interposed between the brazing sheets and brazed thereto, an improved process comprises making at least the fin of a heat-treatable (age-hardenable) aluminum alloy in the Al-Mg-Si system containing 0.15 to 0.4% copper, assembling the fin with said brazing sheets into a brazed aluminum fin heat exchanger unit, maintaining the heat exchanger unit at a temperature between 500.degree. C. and 570.degree. C. for a time from 30 minutes to 4 hours, quenching the solution-treated unit to room temperature under cooling conditions which provide a cooling rate between 2.8.degree. C./min. and 50.degree. C./min. down to 200.degree. C. and thereafter, age-hardening the quenched heat exchanger unit. The above heat-treatable aluminum alloy in the Al-Mg-Si system is AA 6951 or AA 6061.