Depending upon the size of your bin and the heat thrown off by your pump, you might want to invest in a heat mat/thermostat to bring/keep the water up to a higher temp. Perhaps an inverted clear cup on each cutting to trap more heat?
If the water is warm enough (but not too warm), I'd guess that the overall temp and radiating effect from the water would keep the cuttings safe and happy.
I'm no expert, however, so this is just an opinion. My basement is warmer that 40 at night and my cloner has produced some terrific results thus far.
Andrew