How to reuse the same connection with a Spring’s JdbcTemplate?

Spring provides a special DataSource that allows you to do this: SingleConnectionDataSource

Changing your code to this should do the trick:

SingleConnectionDataSource dataSource = new SingleConnectionDataSource();
....
// The rest stays as is

For use in multi-threaded applications, you can make the code re-entrant by borrowing a new connection from the pool and wrapping it around the database-intensive section of code:

// ... this code may be invoked in multiple threads simultaneously ...

try(Connection conn = dao.getDataSource().getConnection()) {
    JdbcTemplate db = new JdbcTemplate(new SingleConnectionDataSource(conn, true));

    // ... database-intensive code goes here ... 
    // ... this code also is safe to run simultaneously in multiple threads ...
    // ... provided you are not creating new threads inside here
}