Certain query operations such as sort or hash table require some memory facility. This memory is provided by a runtime config work_mem.
From the official documentation work_mem

work_mem (integer)
Sets the base maximum amount of memory to be used by a query operation (such as a sort or hash table) before writing to temporary disk files.
Note that for a complex query, several sort or hash operations might be running in parallel; each operation will generally be allowed to use as much memory as this value specifies before it starts to write data into temporary files.
Sort operations are used for ORDER BY, DISTINCT, and merge joins. Hash tables are used in hash joins, hash-based aggregation, result cache nodes, and hash-based processing of IN subqueries.

Once the set work_mem is exceeded, the operation starts writing to the temporary disk files.

Another operation that can write temp files is CREATE INDEX. This is controlled by a different runtime config maintenance_work_mem.
From the official documentation maintenance_work_mem

maintenance_work_mem (integer)
Specifies the maximum amount of memory to be used by maintenance operations, such as VACUUM, CREATE INDEX, and ALTER TABLE ADD FOREIGN KEY.

The particular location where these temporary disk files are written to is controlled by runtime config temp_tablespaces
Again from the official documentation temp_tablespaces

temp_tablespaces (string)
This variable specifies tablespaces in which to create temporary objects (temp tables and indexes on temp tables) when a CREATE command does not explicitly specify a tablespace. Temporary files for purposes such as sorting large data sets are also created in these tablespaces.
The value is a list of names of tablespaces. When there is more than one name in the list, PostgreSQL chooses a random member of the list each time a temporary object is to be created; except that within a transaction, successively created temporary objects are placed in successive tablespaces from the list. If the selected element of the list is an empty string, PostgreSQL will automatically use the default tablespace of the current database instead.
When temp_tablespaces is set interactively, specifying a nonexistent tablespace is an error, as is specifying a tablespace for which the user does not have CREATE privilege. However, when using a previously set value, nonexistent tablespaces are ignored, as are tablespaces for which the user lacks CREATE privilege. In particular, this rule applies when using a value set in postgresql.conf.
The default value is an empty string, which results in all temporary objects being created in the default tablespace of the current database.

Default tablespace vs Specific temp tablespaces

Default installation of PostgreSQL has default tablespace(pg_default) set as the temp_tablespaces.
You might want to separate writes of actual data from temp files, improving disk IO. That is where temp_tablespaces is most useful.
Also, you can point your temp_tablespaces to a faster disk such as nvme which is faster.

Setting up a tablespace for temporary files

You can use the following sample code to set up temp_tablespaces

• Create a new tablespace: ```

CREATE TABLESPACE temp LOCATION 'actual_location';

- Set cluster-wide `temp_tablespaces`:

ALTER SYSTEM SET temp_tablespaces = 'temp';
SELECT pg_reload_conf();

##### Caveats of temp files
1. Temp files can use up the available disk space when a query needs to create a lot of temp files, with PostgreSQL reporting an error such as
`could not write block .... of temporary file no space left on device ...` and the query being canceled.
2. Temp files are only kept around for the duration of a query. Once the query finishes or cancels, the temp files are cleaned up. 
Once in a while DBAs experience (1) and when they check the disk usage, they find out there is still space and start troubleshooting for where the issue might be. The issue is described in (2). When this happens, it might be high time you optimized your queries. The other workaround would be, using a larger free disk as your `temp_tablespaces`. 

##### Monitoring temp files usage
We can log temp files with the help of a runtime config [log_temp_files](https://www.postgresql.org/docs/14/runtime-config-logging.html#:~:text=change%20this%20setting.-,log_temp_files,-(integer))
> `log_temp_files (integer)`
Controls logging of temporary file names and sizes. Temporary files can be created for sorts, hashes, and temporary query results. **If enabled by this setting, a log entry is emitted for each temporary file when it is deleted**. A value of zero logs all temporary file information, while positive values log only files whose size is greater than or equal to the specified amount of data. If this value is specified without units, it is taken as kilobytes. The default setting is -1, which disables such logging. Only superusers can change this setting.

While `log_temp_files` logs information about a temporary file when it is deleted, you might want to monitor the temporary file while it's being created as well, keeping an eye on things.
Also, you might want to know which queries are making use of temporary files and maybe optimize them for the faster `work_mem`.

We would be doing this from SQL.
Query:

WITH tablespaces AS (
SELECT
spcname AS tbl_name,
coalesce(nullif(pg_tablespace_location(oid), ''), (current_setting('data_directory') || '/base')) AS tbl_location
FROM pg_tablespace
),
tablespace_suffix AS (
SELECT
tbl_name,
tbl_location || '/pgsql_tmp' AS path
FROM tablespaces
WHERE tbl_name = 'pg_default'
UNION ALL
SELECT
tbl_name,
tbl_location || '/' || path || '/pgsql_tmp'
FROM tablespaces, LATERAL pg_ls_dir(tbl_location) AS path
WHERE path ~ ('PG_' || substring(current_setting('server_version') FROM '^(?:\d.\d\d?|\d+)'))
),
stat AS (
SELECT
substring(file from '\d+\d') AS pid,
tbl_name AS temp_tablespace,
pg_size_pretty(sum(pg_size_bytes(size))) AS size
FROM tablespace_suffix, LATERAL pg_ls_dir(path, true, false) AS file,
LATERAL pg_size_pretty((pg_stat_file(path || '/' || file, true)).size) AS size
GROUP BY pid, temp_tablespace
)
SELECT
a.datname,
a.pid,
coalesce(size, '0 MB') AS temp_size_written,
coalesce(temp_tablespace, 'not using temp files') AS temp_tablespace,
a.application_name,
a.client_addr,
a.usename,
(clock_timestamp() - a.query_start)::interval(0) AS duration,
(clock_timestamp() - a.state_change)::interval(0) AS duration_since_state_change,
trim(trailing ';' FROM left(query, 1000)) AS query,
a.state,
a.wait_event_type || ':' || a.wait_event AS wait
FROM pg_stat_activity AS a
LEFT JOIN stat ON a.pid = stat.pid::int
WHERE a.pid != pg_backend_pid()
ORDER BY temp_size_written DESC;

Example output:

(8 rows)

Time: 2.960 ms

Finally, there is a new function [pg_ls_tmpdir](https://www.postgresql.org/docs/12/functions-admin.html#:~:text=pg_ls_tmpdir(%5Btablespace%20oid%5D)) available from PG12. I decided not to use this function in the above query because it is not available in lower versions.