How to keep a lager cool

In the south, especially this mild winter, it's hard to keep fermenters cool. I'm about to try a Pilsner with Saflager W-34/70 Dry Lager Yeast and from what I've read, the best temp for this is 48-59 degrees.
I plan on using a very good quality ice chest with frozen gel packs replaced at least twice a day (prolly too much for a beer that is not my fav). I think I can get it to the upper 50's from reading other folks who've tried this.
But, if I put some ice under the fermenter, will that be too cold and possibly kill off the yeast that settle? I now that true lager yeast is bottom fermenting and I plan on trying to keep this temperature for at least 3 and hopefully 4 weeks.
I don't have a fridge I can use and am not sure what else I can try.

I have done this before. I used a wheeled 70qt cooler like this:

http://www.amazon.com/dp/B000F6UJ5K/?tag=skimlinks_replacement-20


I then replaced the lid with 3 layers of white foam insulation and a hole in the top for the airlock. Water surrounded the carboy, so as to make the mass of the whole thing even bigger and harder to change temps too fast. I could get it down to the low 40's doing this method in the summer. And yes, summers are hot here too! I did have this in a room with ambient temps of 76 degrees so I am sure that helped too. To get it colder just use more ice packs or use frozen water bottles. One it is at the temp you want it, then replace 3-4 of them every 12 hours and the temps will be relatively constant.

It works well if you have nothing else.

I use the Igloo 60 Ice Cube filled with water around my fermenter (swamp cooler). I've filled some 2 qt Gatorade bottles with water and a small amount of salt. Swap out a 2qt bottle every 12 hours like clockwork, and you'll be able to hold 50 degrees in a 70 degree ambient very easily, with only a 1-2 degree temperature swing. Put a splash of bleach in the swamp cooler water too, it'll get nasty over the several weeks of fermentation. This works really well, as long as you have a regular schedule to swap out ice.

i'm currently fermenting an Alt with Kolsch yeast like this/URL] and holding 55 degrees. before racking to a keg to lager, i plan on cooling it down to ~45 with some more ice. Stauffbier actually lagered a beer in the swamp cooler. took a mountain of ice bottles, but he got 'er done!