We consider the turbulent energy dissipation from one-dimensional records in experiments using air and gaseous helium at cryogenic temperatures, and obtain the intermittency exponent via the two-point correlation function of the energy dissipation. The air data are obtained in a number of flows in a wind tunnel and the atmospheric boundary layer at a height of about 35 m above the ground. The helium data correspond to the centerline of a jet exhausting into a container. The air data on the intermittency exponent are consistent with each other and with a trend that increases with the Taylor microscale Reynolds number, R(lambda), of up to about 1000 and saturates thereafter. On the other hand, the helium data cluster around a constant value at nearly all R(lambda), this being about half of the asymptotic value for the air data. Some possible explanation is offered for this anomaly.