We report on measurements of the switching current distributions on two-dimensional superconducting NbTiN strips that are 5 nm thick and 80 nm wide. We observe that the width of the switching current distributions has a non-monotonous temperature dependence, where it is constant at the lowest temperatures up to about 1.5 K, after which it increases with temperature until 2.2 K. Above 2.5 K any increase in temperature decreases the distribution width which at 4.0 K is smaller than half the width observed at 0.3 K. By using a careful analysis of the higher order moments of the switching distribution, we show that this temperature dependence is caused by switching due to multiple fluctuations. We also find that the onset of switching by multiple events causes the current dependence of the switching rate to develop a characteristic deviation from a pure exponential increase, that becomes more pronounced at higher temperatures, due to the inclusion of higher order terms.