I have seen this problem on the forums before as well as other channels and my attempt at fixing has not been successful.
The volvo always starts when it is cold, but won’t restart even 1 minute after turning off.
On the restart attempt, it sounds as like the starter motor is spinning, but not engaging.
We turn it over a couple of times, then it engages, then it fails to engage again, or engages slightly, then drops the engagement (no turn over).
Changed the coolant sensor on top, no change.
Codes show a that the rear heat sensor (also changed) is still not work, (the one on the manifold), and also a power supply issue with the ‘motor pump’.
Thinking this may be a fuel pump issue, I am trying to find where this top is covered in the Haynes manual (unless the fuel pump needs to be replaced in it’s entirety).
Either the linkage in the nose of the starter is worn and jambs when hot, or the solenoid is failing (more likely). A new (rebuilt) starter complete with solenoid for that car will run about $100. The solenoid will run at least $30. You can take the starter off and examine the linkage for looseness/wear, but I would get the whole assembly and bolt it on…