The temperature dependence of the linear thermal expansion coefficients (LTEC) of a single crystal of a-(BEDT-TTF)2NH4Hg(SCN)4 where BEDT-TTF is bis(ethylenedithio)tetrathiafulvalene was studied by the method of precision capacitive dilatometry in the temperature range 2-250 K along the crystallographic direction b* (perpendicular to the crystal layers). Negative values of LTEC were found below 4 K. Probably it is due to charge fluctuations as the temperature approaches the temperature of transition to the superconducting state Tc. It has been suggested that the bends on temperature dependence of LTEC observed in the temperature range 25-45 K are related to order-disorder arrangement of NH4+ ions. Weak maximum of the LTEC, detected at a temperature of about 200-220 K, can be caused by the processes of charge redistribution and the associated intermolecular interaction fluctuations.