How much do I have to worry about temperature fluctuations?
More than you think. Temperature fluctuations are what cause our little yeasties to produce off-flavors and also cause them to go dormant. If you have a temp swing of, say, 3 degrees F - that is not a big deal. Temp swings of 10F or more can do a lot of damage to your desired fermentation.
The swing up will cause the yeast to produce more esters (not desirable in ta lager) and the swing down will cause the yeast to get sleepy, go dormant and then cause a stuck fermentation. Neither of these is desirable.
Look up the STC-1000 (or "eBay temp controller") and you'll see that a $20 controller will solve your problems.