When a circuit exhibits a jump like you are describing it is because it has solution curve that has folds in it, as shown with the solid line below.
![](http://www.designers-guide.org/Images/hysteresis.gif)
Here the horizontal axis represents temperature and the vertical axis represents a signal value, say the output voltage.
Starting from the left, the temperature increases until it reaches the lower fold, at which point the output voltage jumps discontinuously. In this case it jumps up to the upper part of the curve (dashed upward facing arrow). If the temperature then began to decrease, the output voltage would stay on the upper part of the curve until it reached the upper fold, at which point it would jump down to the lower part of the curve (dashed downward facing arrow). In this way, the voltage/temperature curve would exhibit classic hysteresis.
If you started at a point between the two folds, then going up you would see a jump, but going down you would not because the upper fold occurs at a temperature less than -40C.
You are almost correct in your belief that DC sweeps are memoryless. To speed up DC sweeps, Spectre extrapolates from the previous solution point to the next. It then starts the DC iteration from the extrapolated point. This tends to cause Spectre to faithfully follow the curve as long as it can. It is this extrapolation that represents the memory in the DC sweep.
-Ken