A cryogenic research apparatus to measure the movement of electrons under a high electric field in a liquid helium bath was designed and built at the Brookhaven National Laboratory and the Nevis Laboratory of Columbia University. The liquid helium chamber is a double walled cylindrical container equipped with 5 optics windows and 10 high voltage cables. To shield the liquid helium chamber against the external heat loads and to provide the thermal uniformity in the liquid helium chamber, the double walled jacket was coolde by a pumbed helium bath. The helium chamber was built into a commercial LN2/LHE cryostat. This paper presents the design and the numerical simulation analysis on thermal uniformity of the electron bubble chamber.