Lager fermenation temp

So I started an oktoberfest beer yesterday, I'm making a Spaten clone with a couple substitutions, but to the point. I stuck a thermometer in a spair not plugged in fridge yesterday and it was a perfect temp of 55 right now the temp is at 63ish and it wasn't a hot day by any means, I'm not sure why the temp is so high in the fridge I am pretty sure it was hotter yesterday but anyways. Is mid 60's too warm for a lager?

I should mention that it seems to be fermenting very well, about an inch of foam and a bubble every 3/4 sec or so.

Fermentation produces heat. I'm not sure if that would account for the change. Sounds like you need a temp. controller for that fridge.

I thought the heat might be from the fermentation but wasn't sure, it makes sense so I am sure thats the problem. My problem however is that I have no outlet for the fridge and my kegorator has a keg in it so I can't use that, I am thinking that tossing a bag of ice in there might keep the temp down. Any suggestions?

well ice could definetly help cool it down, I 've found that if you put it in a water bath that can help insulate it from quick, drastic changes.