Waste heat with both high and low temperatures

[Lindagabi99]

Hi, I'm new to posting. I am working on a current project where I'm suppose to recover heat waste that has for the most part low temperatures but every now and then the temperature peaks so that the temperature is high for a while. The heat waste is going to be used for heating spare rooms. My question is: Is it possible to use (take advantage of) the peaks of high temperature? How does one go about when doing so?

 

[mfb]

It is hard to tell if the description is so vague.
The temperature of what? What is "low" and "high" temperature? How long is "a while"?

It might be possible to get some mechanical or electrical energy out of it and drive a heat pump with that, but the temperature difference should be high to be worth the effort.