The setting of the BT IP profile is automatic, and can't be overridden by ISPs. BT can set a speed cap on a connection, effectively converting it to a fixed-speed connection, but this would be a semi-permanent change, not something which they would swap about every day.
What the ISP can do is apply their own equivalent to the IP profile as part of their traffic management policies, but this wouldn't show up as a change of IP profile when using the BT speed tester.
If your IP profile as seen in the BT speedtester changes between day and night every day, then I'm afraid I can't explain it other than by Kitz' suggestion that you are accidentally picking up someone else's network. Is it possible that the PC has a wireless dongle connected, and you're somehow switching over to using this from time to time?