There have been significant changes in the DB schema between TFS 2010 and 2013. This means that as part of an in-place upgrade process a good deal of data needs to be moved around. Some of this is done as part of the actual upgrade process, but to get you up and running quicker, some is done post upgrade using SQL SPROCs. Depending how much data there is to move this can take a while, maybe many hours. This is the cause the SQL load.
A key factor as to how long this takes is the size of your pre upgrade tbl_attachmentContent table, this is where amongst other things test attachments are stored. So if you have a lot of test attachments it will take a while as these are moved to their new home in tbl_content.
If you want to minimise the time this takes it can be a good idea to remove any unwanted test attachments prior to doing the upgrade. This is done with the test attachment cleaner from the appropriate version of TFS Power Tools for your TFS server. However beware that if you don’t have a suitably patched SQL server there can be issues with ghost files (see Terje’s post).
If you cannot patch your SQL to a suitable version to avoid this problem then it is best to clean our old test attachments only after the while TFS migrate has completed i.e. wait until the high SQL CPU utilisation caused by the SPROC based migration has completed. You don’t want to be trying to clean out old test attachments at the same time TFS is trying to migrate them.