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."
Thomson was given the last five minutes of the Clydesdale Bank Premier League match and was thrilled just to be back in action.
He said: "I was delighted to get back out there. I love playing football and I want to play football.
"It's the first time I've been on the park for seven or eight weeks so it was nice to come on and the reception was really touching."
The derby clash proved to be controversial when a Leigh Griffiths free-kick that clearly crossed the line was not given by the match officials.
Thomson - who was warming up behind the goal at the time - said: "It was miles in. I was right on the by-line when he shot.
"It was obviously in and it was a great free-kick so it's just unfortunate for Leigh and the boys after putting in so much effort and not getting three points.
"It's part and parcel of football. It's frustrating when they go against you.
"There wasn't much in the game. It was nip and tuck with half chances at either end and a draw is probably a fair result."
Asked for his own view of the disallowed goal, Hearts goalkeeper Jamie MacDonald said: "It was a good strike but I honestly couldn't tell you if it was in.
"It happened and it's part and parcel of football.
"It's maybe a bit of luck for us. There have been a lot of instances this year where luck has gone against us so we will take it.
"I thought we should have had a penalty that we didn't get so it evens itself out and you can look at it that way. It's probably a fair point overall."