I'd say the "high flow" nature of the new t-stat had more of an effect than the new temp rating. And bear in mind that with a 160 it will begin to open sooner, so it takes longer for the engine to reach a higher temp, so a longer drive in that hotter weather will give you a better idea. Keep in mind an OEM type replacement t-stat was probably not designed with a high flowing Desert Cooler in mind. Nice radiator like a Desert Cooler needs as much flow as it can get to really shine, whereas an OEM radiator uses much smaller passages and is probably designed around a lower flow rate.
Car T-stats are pretty much just like the one in your house, either system it's attached to has the capability to do what the t-stat asks it to do, or it doesn't. If the AC in a house won't cool the house to 68 degrees, turning it to 60 won't make a difference.
But of course the T-stat in a house doesn't alter flow like it can in a car
