There is little difference between temporary and permanent cross border service provision in Norway. The procedures for temporary service provision in Norway are very similar to those for establishing a permanent business. A Norwegian organisation number would therefore generally be required in order to provide services in Norway.
In this respect, legislation and regulation is different in Norway compared to countries in EU, mainly because Norway is an EEA country, but not an EU member state. Norway is also not a member of the European VAT union as defined by the VAT Directive. As a consequence, businesses very often need to register for VAT in Norway.
All persons holding positions identified by the Coordinated register notification, e.g. the general manager and those authorized to sign for the company, shall be identified by a personal identity number/D-number/organization number, personal name/name of enterprise and address. Hence, foreign citizens without a Norwegian personal identity number must apply for a Norwegian D-number.
The duration of the business and the form of organization will help determine in which country the taxation should take place. The tax liability is determined by the Central Office - Foreign Tax Affairs. Further readings "Tax in Norway"
Note that you may need special permits/licences to operate a business in certain sectors.