It has been ascertained that the slip-initiation in iron-foil under fatigue is almost dominated by the linear cumulative damage rule ∑ni/Ni=1 irrespective of temperature rise or fall when the ambient temperature varies stepwise. In this paper, in order to establish the rule dominating the slip-initiation under the condition of continuous temperature change, the validity of an integral form of the rule, ∫(1/N)dn=1, was examined by the tests in which the temperature was varied linearly in the low temperature range. The following conclusions were drawn from the results obtained. The linear cumulative damage rule ∫(1/N)dn=1 almost holds for the slip-initiation under the condition that the temperature varies linearly at low temperatures irrespective of temperature rise or fall. Therefore, it is considered that the rule is applicable to the slip-initiation under any temperature variation in such a temperature range that strain aging does not occur in iron-foil.