problem with fridge temp, first lager ferment

Hey all, I've brewed my first lager this Friday and threw it into the fridge after chilling to about 98F. After waiting about 8 hours I pitched a 3 liter starter of WY2124. The thermometer I put in the fridge read 62-64F at that time. The problem is that it's now 24 hours later and the temperature is still reading at 62F. I thought it would have cooled a bit more by now as I had the thermometer in the fridge for a week prior and was able to keep it steady at 50F.

I've got the temperature dial set to the coldest setting but it doesn't look to be dropping the temp any. The beer is bubbling away but I am worried about ruining it at this high a temp. Should I try freezing some water bottles or try waiting it out a bit longer? Also, I've pitched this about 24 hrs ago and it's been pretty much steady at 62F in the fridge. I'm wondering how much time I still have to maybe save this beer before the ester production gets out of hand.

What is this "fridge" you are referring to? I have no idea if it is a mini-fridge, a commercial fridge or a stand up freezer.

Based on what you're saying, it is undersized for the job and you don't have a temperature controller on it. Is that right?

It is a regular sized home fridge, not a commercial but not a mini. And yes, not currently using any kind of temp controller, but I do have an STS love controller I have mostly wired, just need to order an appropriate thermowell on ebay. What I've done so far is to put the fermentation bucket in my 10 gallon kettle, where there is just enough clearance on the sides to dump ice into, which I have been doing every 12 hours and the temperature inside the fridge has dropped to 51-52F. I'm going to take a temperature and gravity reading of the beer tomorrow.

is the fridge running continuously? and you mean the kettle/ice/bucket are in the fridge? thats probably as good as you can do.

the design of the fridge might be causing trouble. if it has a thermometer that is reading much colder than where you put a thermometer, also much colder than the bucket, the fridge might be shutting off. or taking ice out of the freezer might be drawing cooling away from the fridge.