Basis is the heat exchange rate in the sample chamber.  We want to deliver (extract) heat that will change the liquid temperature at some given rate.  It is assumed that mixing in the chamber is instanteneous.

    Define:    F - flow rate in liters per minute
                  del_T - difference between temperature of incoming liquid and current chamber temperature
                  V  -  volume of liquid in the chamber (liters)
                  cr - cooling rate per minute
                  s  -  specific heat of liquid; cancels out anyway so no value needed

    Then, (neglecting the heat removed by the outgoing fluid, i.e. its del_T is zero):
 
                            F . del_T  . s = V . cr  . s

    So, for V = 4 L, del_T = 10 and cr = 2 C/min  we get  F = 0.8 L/min

    The assumption is that the incoming fluid is 10 C colder than the chamber temperature.  At a chamber temperature of -20 C and bath temperature of -35 C this may be possible (depends on the efficiency of the heat exchanger in the bath).  If we make the more conservative estimate of del_T = 5, the flow rate needed goes up to 1.6 L/min