Modern helium liquefaction / refrigeration systems employ compact plate-fin heat exchangers having very high effectiveness (>0.95). Performance of such systems is a strong function of effectiveness of heat exchangers used. The calculation of heat exchanger effectiveness in such cases needs considerations of several secondary parameters apart from basic fluid film resistance. In the present paper, the combined effects of secondary parameters like axial heat conduction through heat exchanger matrix and parasitic heat in-leak from the surroundings has been studied numerically. Large temperature changes in cryogenic heat exchangers may result in correspondingly larger changes in fluid properties and metal matrix conductivity, which shall be taken care of during numerical calculations. Numerical model developed in the present work is based on the one given in the literature. Numerical technique to solve the system of equations is implemented in MATLAB^®. Real properties of helium at each node are evaluated using HEPAK^®, which is linked to the developed code. Using this model, performance of heat exchangers is studied at four different temperature levels of (300-77)K, (77-20)K, (20-8)K and (10-5.1)K. The results highlight the effects of each of the above secondary parameters.