Running without a thermostat ok?

Few months ago replaced the radiator, water pump, thermostat, hoses, etc. Had a 160* thermostat and when cold weather came in, upped it to a 180* to get more heat flowing. She's always run around 180*-185*. As the temps rise, I've noticed she's running hotter as the heat rises. When it was 80* she ran about 185* 85-90* outside, it started rising to 190*. 90-95* around 195*. Temps hit 97* today and she ran as high as 200*+. Same road, same driving every day back and forth to work. No sign of lower temps so I expect it to just keep climbing. Everything seems to be working ok, she cools down at 45-50mph and idling at stop down to around 185+* or cruising on shady roads. As she starts uphill and I maintain speed, the temps start climbing. Question is, is it ok to run without a thermostat or should I just drop it back down to a 160* and see that provides enough coolant flow to keep her down to under 200*? I expect 100*+ temps in a couple of days. Any and all input is greatly appreciated.