Questions about startup behavior and hot/cold data rules with TSI index in InfluxDB 1.x

Background:
I'm using InfluxDB 1.x with TSI (tsi1) index enabled.

Observation:
When the database starts up, it scans through all TSM files. This seems to take a significant amount of time, especially with a large dataset.

Core Question:
According to the official documentation, TSI leverages the operating system's page cache to manage hot data, keeping frequently accessed index data in memory while cold data remains on disk. However, I couldn't find a clear explanation of how "hot" and "cold" data are actually determined.
How can I improve InfluxDB's startup speed when there are a large number of shards?

Start with the official InfluxDB 1.x documentation for TSI, then trace the startup scan behavior for TSM files and multiple shards. Document how hot and cold index data are determined and identify supported ways to improve startup time; the issue does not name a documentation file or test.

Written by the indexing model from the issue text.