We　propose　a　scheme　for　realizing　two-qubit　quantum　phase　gates　with　trapped　ions　in　thermal　motion.　In　the　scheme,　the　ions　are　simultaneously　illuminated　by　a　standing-wave　laser　tuned　to　the　carrier,　which　virtually　excites　several　vibrational　modes.　The　scheme　puts　no　limitations　on　the　intensity　of　the　laser　field,　allowing　the　production　of　a　quantum　logic　gate　for　hot　ions　with　an　arbitrarily　high　speed　as　long　as　a　laser　field　of　sufficiently　high　intensity　is　available.　©　2003　The　American　Physical　Society.