Do you mean the "Method Hotspots" or "Response Time Hotspots" views when looking at a service? These analysis views are not available over the API.
I think your best bet would be to open a request for enhancement. If you don't mind could you explain your use case for this?
The use case is, of course, to automate the process of finding out what is impacting the systems being monitored, and "talk" to Davis before real problems happen 🙂
While you cannot extract Hotspot information via the Dynatrace APIs, you can extract performance metrics (such as wait/lock/cpu/IO time) to get an understanding of what type of time, and thus what sort of issue, could be contributing to services/key requests experiencing slow downs.