Is it ok to move a ferment bucket in diff environments

So, I'm getting ready to make the Cheesehead caramel cream ale.

I recently discovered that my minifridge from college will fit a ferment bucket perfectly, and brought to my loft. I still need to acquire a thermostat control to get it to raise to the right temperature.

I have both Wyeast german ale liquid and dry, and according to their website, the range is 55 to 68 degrees. My minifridge at the lowest setting is ~44 degrees.

I guess i'll start this batch (tuesday) in the bucket and put in a big plastic hamper waterbath. I'd like to, if its ok for the fermenting activity, to move it from the water bath to my minifridge once the temperature can be managed correctly.

So long as I do not slash, would it be an issue to move it?

No, not as long as the two environments are basically the same temperature. Depending on how soon you move it, the bulk of fermentation may be done.

As long as you don't go spashing it around.....ain't no big thing.