PostgreSQL "size of temporary files"
I found nothing in the pgAdmin documentation, but the source code reveals the query behind these entries (added for Postgres 9.2+):
It boils down to:
SELECT temp_files AS &quot;Temporary files&quot;
     , temp_bytes AS &quot;Size of temporary files&quot;
FROM   pg_stat_database db;

And the Postgres manual has details for pg_stat_database:

tmp_files bigint  Number of temporary files created by queries in
this database. All temporary files are counted, regardless of why the
temporary file was created (e.g., sorting or hashing), and regardless
of the log_temp_files setting.
temp_bytes bigint     Total amount of data written to temporary files
by queries in this database. All temporary files are counted,
regardless of why the temporary file was created, and regardless of
the log_temp_files setting.

Note that these values do not contribute to the size of your database. But they indicate that your setting for work_mem may be too low, so that many sort operations spill to disk (which is very slow as compared to just RAM).
Related:

Optimize simple query using ORDER BY date and text

To actually compact the size of your database:

VACUUM returning disk space to operating system

To measure size:

Measure the size of a PostgreSQL table row

Aside: WAL (Write Ahead Log) would be equivalent in Postgres for the transaction log in SQL Server. Nice explanation in this related answer on SO:

Why do SQL databases use a write-ahead log over a command log?