There are no specific parameters like that, but the net effect of how GNSS works has a similar effect. To simplify (and assuming a valid almanac is in place), then downloading position data from a satellite is what causes the "delay" in acquiring a lock - you first need to know where the visible satellites are to calculate where you are, and that satellite location data download (ephemeris data) from the satellite can take 30 seconds or more. This is a "warm start" if this happens. Ephemeris data is regenerated approximately every four hours, so depending on when it was generated and when you receive it, it could be valid to you for less than that. This data can be cached once downloaded, however, and when the receiver starts up later, it can check to see if it has valid cached ephemeris data for all the satellites it sees. If it does, then it can provide a lock "instantly", called a "hot start".
So, what changes this ability to do a "hot start"? On starting the receiver, if the same satellites are visible, but enough time has passed such that the cached data is no longer valid, it needs to re-download this data, pushing you into "warm start" timeframes.
Additionally, satellites are orbiting, and rise and set approximately twice a day for a given location. When starting the receiver, even if the timeframe is within the valid cached data timeframe, one of the previously-seen satellites may have orbited beyond visibility, and a different satellite in that orbital plane is now in view, for which you have no cached data, requiring the download and "warm start". Similarly, if you move a significant distance, that can change which satellites are now visible, especially given the timeframe to move, so when starting the receiver up, the chances of seeing the same satellites, and the cached data being still valid timewise, are significantly reduced.
So, there are no "hard" parameters set for a "hot start", it's basically - do you have valid cached ephemeris data for all the satellites you can see. The passage of time affects the validity of the cached data and the visible satellites as they orbit, and the moving of a significant distance affects the visibility of the same satellites even if you could move instantaneously; but as they also orbit in the time taken to move a significant distance, this increases the odds of the visible satellites changing.
Here's a dump of data of the GPS satellites seen by a uBlox M8 chip on my desktop right now (it's the GNSS chip used in just about every DJI drone from the
P4Pro to the
Air2S), to give you an idea of what the GNSS system "sees":
View attachment 143951
You can see that satellites G8, G16, G26, G27 and G31 are visible and the current ephemeris data is good for another 2.5 hours. G9 is visible, but no ephemeris download yet. G25 is no longer visible, and the cached data is good for 0.5 hours. G31 is in visible state of "EL", which means it's elevation is low to the horizon and it will soon orbit out of view. If I were to restart the GNSS chip within 10 mins, I may or may not get a "hot start", depending if G31 orbits away. If I restarted it 3 hours later, I would not get a "hot start" as none of the cached data is valid for that long. If I teleported to the opposite side of the planet instantly, none of those sats would be visible and it'd be a "warm start" while I wonder how the hell I just teleported to the other side of the world