If you are super user you can execute whatever template via API
Updated the exisitng /service/template/results to accept the optional parameter userName representing the username whom template belongs to.
Example:
curl "http://localhost:8080/biotestmine/service/template/results?name=template2&userName=test@intermine.org&constraint1=Gene.chromosome.primaryIdentifier&op1=eq&value1=MAL1&format=tab&size=10&token={super user's API token}"