As mentioned by @abhiklpm using $_SESSION and '#default_value' from FAPI can do the trick.
Something like, after first form submission grab values you want to autofill and put them into current session simply by doing. Assuming 'first_name' and 'last_name' are form fields.
$values['first_name'] = 'test';
$values['last_name'] = 'test2';
$_SESSION['module_name']['my_multistep_form'] = $values
Alter the second form to add '#default_value' property to form elements.
$form['first_name']['#default_value'] = $_SESSION['module_name']['my_multistep_form']['first_name'];
$form['last_name']['#default_value'] = $_SESSION['module_name']['my_multistep_form']['last_name'];
Remember to unset values from $_SESSION in second form submit handler, use
unset($_SESSION['module_name']); to unset the session.
You might want to have a look on ctools multistep forms as well
http://internetdevels.com/blog/ctools-multistep-wizard-example .