H81 motherboard replacement processor generally does not need to update the BIOS.
The compatibility of the h81 motherboard with the new processor is relatively good. However, some early motherboards may require a BIOS refresh when using E3 v3 series processors.
In order to avoid unnecessary trouble, upgrade or replace the processor at least from the official website to check their own motherboard model and the corresponding BIOS model. Get relevant information so you can be targeted.