What are the consequences ? Because this file will be remove if the server reboot.
Those temporary statistics are stored in global directory when server shuts down, so the risk here would be to lose a portion of this data in the case of a crash, either at PG or at OS level.
If we change the parameter stats_temp_directory is it necessary to reboot the server ?
No, sending SIGHUP to the server is enough.
When I lauch a SHOW ALL; command, the parameter stats_temp_director is not here.
You should get it... stats_temp_directory | pg_stat_tmp | Writes temporary statistics files to the specified directory.