You can get 2nd heart with him by done a event name 'I own you a beer'.
The rest of this I just copy from Wildbara
- Finish Bandit Attack story, Bandit's Camp morale is 25+.
- Finish Full Moon story, must've checked on Logan first!!!
- Start Bareshade Expansion story, finish the More Houses part.
- Visit the Tavern after 20:00, that triggers the fight between Logan and Barrel.
- Finish Bareshade Expansion completely.
- Finish Country Road story, gained from Ste after inviting him to Bareshade.
- Visit Logan during daytime, witness his outburst, visit Bareshade at night and follow him.
- Help him with work during the day.
- Go to your house in Bareshade at night and Logan will visit you, invite him in, refuse to have sex.
By the way, if you can gain his 1st heart. You are in Normal Logan route.