I also would also suggest replacing the thermostat first. They do go bad. I just put a Wahler brand from Fastlane in my '88 260e and the temp holds steady at 84^, of course it hasn't been very warm here in Illinois yet. Another possibility is that you have air trapped in the cooling system. Thermostats are supposed to have a small jiggle valve that allows air to vent. Sometimes that valve gets corroded shut. That would explain why your problems started after your coolant was drained.

Good Luck.