diff --git a/README.md b/README.md
index 73917db..e7eabe1 100644
--- a/README.md
+++ b/README.md
@@ -62,6 +62,8 @@ export WPT_TEST_DIR=wp-test-runner-$TRAVIS_BUILD_NUMBER
 export WPT_TABLE_PREFIX=wptests_$TRAVIS_BUILD_NUMBER\_
 ```
 
+The test suite's temporary files are kept in a `wp-temp` directory inside the test directory, so runs with their own `WPT_TEST_DIR` do not share the system temp directory.
+
 Connect to a remote environment over SSH by having the CI job provision the SSH key:
 
 ```bash
@@ -272,7 +274,7 @@ export WPT_PREPARE_DIR="/tmp/wp-test-runner"
 
 **Test directory**
 
-Path to the directory where the WordPress develop checkout can be placed and tests can be run. When running tests in the same environment, set WPT_TEST_DIR to WPT_PREPARE_DIR equally.
+Path to the directory where the WordPress develop checkout can be placed and tests can be run. When running tests in the same environment, set WPT_TEST_DIR to WPT_PREPARE_DIR equally. The test suite's temporary files are kept in a `wp-temp` directory inside this path.
 
 
 ```
diff --git a/prepare.php b/prepare.php
index 9473ca2..9cf1cc6 100644
--- a/prepare.php
+++ b/prepare.php
@@ -242,6 +242,34 @@ function curl_selected_bits(\$k) { return in_array(\$k, array('version', 'ssl_ve
 // Replace the placeholders in the wp-tests-config-sample.php file content with actual values.
 $contents = str_replace( array_keys( $search_replace ), array_values( $search_replace ), $contents );
 
+/*
+ * Point the test suite's temporary directory inside the test directory, so
+ * concurrent runs with their own WPT_TEST_DIR do not share the system temp
+ * directory. Core's get_temp_dir() checks the WP_TEMP_DIR constant first,
+ * and several tests write fixed file names into that directory, so two runs
+ * sharing it can delete or overwrite each other's files mid test.
+ *
+ * The path is anchored to the config file's own location, so it stays
+ * correct after the config is copied to a remote test environment, and the
+ * directory is removed together with the test directory during cleanup.
+ */
+$contents .= <<<'WPT_TEMP_DIR_CONFIG'
+
+if ( ! defined( 'WP_TEMP_DIR' ) ) {
+	define( 'WP_TEMP_DIR', __DIR__ . '/wp-temp/' );
+}
+
+if ( ! is_dir( WP_TEMP_DIR ) ) {
+	mkdir( WP_TEMP_DIR, 0777, true );
+}
+
+if ( ! is_dir( WP_TEMP_DIR ) || ! is_writable( WP_TEMP_DIR ) ) {
+	echo 'The temporary directory ' . WP_TEMP_DIR . ' could not be created or is not writable. Fix the permissions on the test directory and run again.' . PHP_EOL;
+	exit( 1 );
+}
+
+WPT_TEMP_DIR_CONFIG;
+
 // Write the modified content to the wp-tests-config.php file, which will be used by the test suite.
 file_put_contents( $runner_vars['WPT_PREPARE_DIR'] . '/wp-tests-config.php', $contents );