When doing an oil analysis the recommendation is to drain within 5 minutes of stopping the engine i.e. at operating temperature.
If you wait longer than this the particles in the oil start to settle and you may get an inaccurate reading e.g.
https://www.machinerylubrication.com/Read/30107/oil-sample-agitation
You would have exactly the same problem when changing oil. Thus change the oil when it is hot.

"Too often oil samples are taken when machines are at rest (not when they are running). Sometimes this is avoidable, but sometimes it is not. Live oil samples are always best. Circulation keeps the fluid homogenous at the time the sample is taken. Lack of fluid circulation causes particle settling and sedimentation (see Figures 1-4). The longer the delay between when a machine is turned off (stopping oil movement) and when the oil is sampled, the greater the number of particles not received in the sample bottle.
Particles are like data. This data provides important information that can prescribe a needed corrective action. When particles settle out of the oil, you lose data. This lost data may prevent you from being aware of an abnormally high particle count or advanced machine wear condition. This would produce a false negative in the oil analysis results. This means the oil’s condition may be falsely reported to be better than reality.
Evidence of particle sedimentation shows up in oil sumps and reservoir bottoms. Sampling the bottom of the sump or reservoir provides little help since the sludge and sediment that accumulate there are a repository of data spanning weeks, months or even years.
This is not representative of the current conditions, including the health of the oil, the contaminant level of the oil and the active rate of machine wear."
If you wait longer than this the particles in the oil start to settle and you may get an inaccurate reading e.g.
https://www.machinerylubrication.com/Read/30107/oil-sample-agitation
You would have exactly the same problem when changing oil. Thus change the oil when it is hot.

"Too often oil samples are taken when machines are at rest (not when they are running). Sometimes this is avoidable, but sometimes it is not. Live oil samples are always best. Circulation keeps the fluid homogenous at the time the sample is taken. Lack of fluid circulation causes particle settling and sedimentation (see Figures 1-4). The longer the delay between when a machine is turned off (stopping oil movement) and when the oil is sampled, the greater the number of particles not received in the sample bottle.
Particles are like data. This data provides important information that can prescribe a needed corrective action. When particles settle out of the oil, you lose data. This lost data may prevent you from being aware of an abnormally high particle count or advanced machine wear condition. This would produce a false negative in the oil analysis results. This means the oil’s condition may be falsely reported to be better than reality.
Evidence of particle sedimentation shows up in oil sumps and reservoir bottoms. Sampling the bottom of the sump or reservoir provides little help since the sludge and sediment that accumulate there are a repository of data spanning weeks, months or even years.
This is not representative of the current conditions, including the health of the oil, the contaminant level of the oil and the active rate of machine wear."