Heat transfer from a cyclindrical copper surface to liquid helium at 4°K has been measured. The sample consisted of a horizontally mounted 3 mm o.d., evacuated glass tube, 6.5 cm long, onto which was deposited a 2000 Å‐thick copper film. It was heated by passing an electrical current through the copper film, and the temperature was monitored by a carbon resistor attached to the inside of the glass tube with varnish. In initial experiments, large temperature fluctuations were observed in the nucleate boiling region. These temperature fluctuations disappeared when the sample was either close to the liquid helium surface or when vertical walls were placed around the sample. The large temperature fluctuations were probably due to interactions of the convective flow of liquid helium with the boundaries of the system (Dewar walls, liquid surface, etc.). Similar temperature fluctuations were observed with a stainless steel sample of approximately the same dimensions. The peak heat flux obtained in the nucleate boiling regime was 0.98 W/cm2for Cu and 0.66 W/cm2for stainless steel.