When searching for a template from the Quick Profile, by default, the additional argument "customer.organization.id=..." is added to the search criteria.
So, if the Organization of the Affected End User specified in a Template does not match that of the Contact displayed in the Quick Profile, no Template will be returned.
If the Contact shown on the Quick Profile does not belong to an Organization, the Search Argument will be "customer.organization IS NULL".
By default, the initial template search is filtered with the end user's Organization. This behaviour is controlled by the filter_template_search option in the Options Manager.
If you do not want the initial template search to be filtered by the end user's Organization, open the 'Options Manager' in the Administration tab, click on 'Request-Change-Issue' and select "filter_template_search", and Deinstall the option. After this change, you will need to restart Service Desk Manager for the change to take effect.