Hi Natalia,
Currently we couldn't map custom field in PhoneCall Template entity to corresponding custom field in PhoneCall entity in OOB way.
From my test, a workaround would be below:
PhoneCall subject field will be updated with the subject value in PhoneCall Template,
thus we can create a workflow which will be triggered when a PhoneCall record is created,
check if the Subject filed equals specific value.(subject value in specific PhoneCall Template record),
then update custom corresponding field with text content manually.(custom field value in pecific PhoneCall Template record).
You can add more If Conditions if you have multiple phonecall template.
That's the simplest situation if both of your custom fields type are single line text.
Please let me know your custom fields type if the workaround would meet your requirement.
Regards,
Clofly