What is the correct way to write to temp file during unit tests with Maven?

You could try to use TemporaryFolder JUnit @Rule as described here

The TemporaryFolder creates a folder in the default temporary file directory specified by the system property java.io.tmpdir. The method newFile creates a new file in the temporary directory and newFolder creates a new folder.

When the test method finishes, JUnit automatically deletes all files and directories in and including the TemporaryFolder. JUnit guarantees to delete the resources, whether the test passes or fails.

After Question Updated

You can change the working directory used by maven-surefire-plugin.

<plugins>
    [...]
      <plugin>
        <groupId>org.apache.maven.plugins</groupId>
        <artifactId>maven-surefire-plugin</artifactId>
        <version>2.12.3</version>
        <configuration>
          <workingDirectory>${project.build.directory}</workingDirectory>
        </configuration>
      </plugin>
    [...]
</plugins>

You can change that working directory to anything you need for your tests like ${project.build.directory}/my_special_dir/.

The working directory in surefire plugin only affects tests being run and ONLY for tests being conducted by maven. If you run your tests from within an IDE the working directory will be something else.