Ah, I understood. It's because it opens default profile instead of the portable one. I have Thunderbird Portable always running though. When I open html files they open in running FF Portable, but Thunderbird opens new instance with default profile. Can this be fixed?

See if there is a setting in your computer to choose Thunderbirdportable instead of Thunderbird.

Start > Settings > Default Programs Is thunderbirdportable listed ? If yes, select 'thunderbirdportable' and click on 'Set this program as default'.

No, it isn't, only Thunderbird. Now I've edited associations manually in the registry, changing "...\App\Thunderbird\thunderbird.exe" to "...\ThunderbirdPortable.exe" and that solved the issue.