Lager Fermentation

I made an AHS 20th Anniversary Oktoberfest this weekend, my second brew ever! I didn't know what I was really getting myself into with lagering and having to keep my carboy at below 60 degree temps.
Anyways after a slow start with the White Labs WLP820 marzen yeast, I am finally seeing good signs of fermentation with airlock bubbles and krausen forming on top.
I am currently keeping my carboy in a gardening bucket surrounded with ice, water, t-shirt, and towel. There is enough room for ice cubes, but not for 20oz bottles of ice. The problem is my stick on thermometer came off with it being in water for an extended period of time, so I don't really know what temperature the wort is fermenting at? Any suggestions? I think it is probably around 60 degrees, but probably keeps fluctuating because I can't keep an eye on it at all times. Could these fluctuations make any off flavors?
Also once fermentation is complete I plan on moving to my secondary bucket, but should I keep doing what I am doing now? Or just let it sit at room temp, because I would like to keep my stick on thermometer on my secondary?
Thanks for all the help.

60 F is too high for a lager. You need to keep it closer to 50 or below. You'll have all kind of off-flavors fermenting that high

Sent from GT-I9100M

you can get a digital indoor/outdoor thermometer from Home Depot or walmart, the kind with a probe on a wire. tape it to the fermenter above the water level and cover it with bubble wrap, styrofoam or some other insulating material. You can use electrical tape, duct tape, etc. It should read very close to the temp of the beer.

Thanks for the suggestions.
Luckily last night it started getting cooler down here in Mississippi, so I just stuck my carboy and temporary "lager cooler" (described in post before) outside. It got down to like 40 degrees last night and it probably kept the temperature more stable. Even though I still don't have a very accurate value of temperature. Hopefully this one will turn out drinkable.
Should I worry about getting it too cold during fermentation? Will that kill the yeast or make it less active?

Well after two weeks of fermenting I racked my beer into my bottling bucket and then bottled my beer. Hit my FG at 1.012 and my OG was 1.051. Since I didn't have a way to consistently store my oktoberfest at lagering temperatures, I figured I would bottle and let it carbonate and then lager about half of it(maybe all, if it will fit) in my mini fridge or refrigerator. Tasted pretty good when I bottled and I know it will tasted even better with age. I will post an update when it aged a little more.