A word for "rate of change"
Solution 1:
Speed is used for the rate of change of distance with respect to time. Sometimes speed is used in contexts similar to what you mention.
How quickly will the soup reach room temperature.
Solution 2:
I tend to use 'delta', but it's what I call an 'acquired' definition - it's one I picked up along the way, but I have no idea if it's the correct one.