if you're keen on modifying the core then to start you can modify (config.php):
PHP Formatted Code
$_CONF['dateonly'] = '%d-%b';
Change the previous to the following In order to reflect the year as well as just the day and month (which I think a date should do anyway) like so (config.php):
PHP Formatted Code$_CONF['dateonly'] = '%d-%b-%Y';
Then change the code you quoted above to reflect the following (search.class.php):
PHP Formatted Code //$thetime = COM_getUserDateTimeFormat ($A['day']);
$thetime = strftime( $_CONF['dateonly'], $A['day'] );
You can always just define your own custom date format and create a new space for it in the config.php file like $_CONF['mypreferreddateformat'] and then use that in the above snippet.
Or you could add your preferred date format to the database and just select it as default in your site's settings. That would make it a site wide change, but you wouldn't have to modify the core.
I can go on if you like, but that should get you going.