For minor upgrades, the Phorum team has the policy that templates should not change. For example, if you are upgrading version 5.1.1 to 5.1.2, you can simply keep the old templates.
Template functionality might change between major Phorum releases. For example, templates that were made for Phorum 5.0.x are not compatible with the templates for Phorum 5.1.x. So to upgrade these, you'll have to build new templates, based on the new default template that is included in the distribution. Simply copying the old template will most probably result in errors and missing functionality.
If you are doing a minor upgrade and you have to preserve changes that were made to the default template (which is not the recommended way of customizing Phorum, see creating_templates.txt), you can follow one of the following options: