Yes, that would be an issue. You want a nice steady temperature, not fluctuations. You do the primary ferment around 50 degrees, and the lagering in the 30s. If you're doing the primary, and it fluctuates, the yeast might not want to do their job.
__________________ Broken Leg Brewery Giving beer a leg to stand on since 2006
my suggestion would be to ask the seller why it fluctuates with temp. if it is a faulty control, you could just replace it. if there is a problem with the cooling system itself, i don't know what to tell you other than look for another fridge...
Carboy: Apfelwein, aged 11 mo
Mr. Beer: (empty)
Never lagered before, but I came across someone selling an old fridge that apparently doesn't work very well. They told me it cant keep a constant temp too well. Will that be an issue?
An old fridge is perfect for lagering, but you don't want one that doesn't work well. There are so many old fridges people are giving away or selling very cheaply, that you might as well just get one that works decently.