If the drugs are in a sealed glass phial, you could put an open or closed Tupperware type container in the fridge, filled with water and store the phials in the water. The water, once down to the required temperature, would not be so susceptible to temperature fluctuations due to door openings etc.

Same principle as my beer bottles - once down to temp, etc......... except that they don't normally last long enough to suffer from temp variations due to door openings