A racing tyre performs within a narrow band of temperature and pressure, and outside that band its grip falls away sharply. Managing the window is one of the central problems of motorsport.
Rubber grips chemically as well as mechanically
Part of a tyre's grip comes from the rubber deforming around the texture of the road surface, which behaves much like interlocking.
The other part comes from adhesion at the molecular level between rubber and surface, and that adhesion depends strongly on the temperature of the rubber.
Racing compounds are formulated to maximise the second effect at high temperature, which makes them extraordinary when hot and close to useless when cold.
Temperature must be right in two places at once
Surface temperature responds within a corner or two, rising with sliding and falling on a straight, and it governs the immediate level of grip.
Bulk or carcass temperature changes over several laps and determines the pressure inside the tyre as well as how the structure flexes.
A driver can have a hot surface on a cold carcass, which feels grippy but behaves unpredictably, and this mismatch is common on an out lap.
Pressure is set cold to arrive correct hot
Air inside a tyre expands as it heats, so pressure rises substantially between leaving the garage and reaching racing temperature.
Teams therefore set a cold pressure calculated to produce the desired running pressure, which means the tyre is technically wrong until it is warm.
Getting it wrong changes the shape of the contact patch. Too high and the tyre rides on its centre; too low and the shoulders take the load and overheat.
Overheating destroys a tyre faster than wear
Pushing beyond the window causes the surface to become greasy as the rubber begins to break down, which reduces grip and encourages more sliding.
More sliding produces more heat, so the process reinforces itself and a driver can lose a set of tyres within a couple of laps by attacking too hard.
Recovering requires backing off long enough for the surface to cool, which costs time immediately in exchange for saving much more later.
Why warm-up dominates qualifying and restarts
A single fast lap requires the tyre to be in its window at the moment the lap begins, which is why preparation laps look erratic and are carefully choreographed.
Restarts after a neutralised period present the same problem, since the field has been circulating slowly and the tyres have cooled below their operating range.
Cars behave very differently in those first corners, and a large share of incidents occur precisely because grip is far below what the drivers are accustomed to.