Transmission temperature max of 240 deg. sound right?

Thank you for all of your replies as well as the in-depth research. You guys are great. When installing the larger trans. cooler and gauge I also had them flush completely the transmission, put in a new filter and put in BG brand synthetic fluid. The old fluid (about 12,000 miles old) was a little off color which prompted me to make improvements during this vacation. Once I am home I may go to a deeper pan as well. All good suggestions.