An easy aspect of near space to simulate is its intense cold. A styrofoam cooler packed with dry ice does a nice job. But don't let the experiment actually touch the dry ice. Use a cookie rack to hold the experiment above the dy ice. Even colder temperatures can be reached if you add a fan or two to circulate the air Run their power cables outside the enclosure as there's no need to chill the power source of the fans.
Expect temperatures to drop to at least -60 deg F on ascent to near space. Your dry ice chamber shuld be able to get close. Brrrrrr!!!