i'm in the same boat right now. i'm going to make a second starter with the yeast from the first. should give me plenty of viable yeasties to do my bidding. shouldn't be a problem as long as nothing from the fridge contaminated them.
If you had more than a day I would suggest adding some more wort to step it up, check viability, but since you want to use it tomorrow I would decant off the spent wort and let it warm to room temp (12 hours should be good).
I would pour off the beer and add some more wort after you warm up the yeast to room temperature. More than anything to make sure the yeast are still viable.
You would of course make sure everything has been sanitized.