The midfielder sealed his return to Easter Road on Friday after training with his former employers for a spell and he made a late appearance from the bench in a goalless draw with Hearts.
Thomson was a free agent after leaving Middlesbrough in January and has penned the short-term deal until the summer.
He said: "I just want to do my best for the club. Hopefully when we get to the end of the season it will have been a successful couple of months.
"With football, you don't really know what's around the corner. I'll give my all for the next two months and we'll see where we are in the summer."
Budget constraints at the club resulted in Thomson offering to play for free.
He added: "I wanted to help the club. It's probably the only club in Britain that I would play for nothing for.
"It is what it is. I'm here playing for nothing and I'll give my all.
"If people want to praise me for doing that, then great. If not, I'm still going to go about my business and try my best for the team."