consisting of temperature measurements recorded in Nicosia, Cyprus, for the winter period, December 2006 to beginning of March 2007 and for the summer period, June 2007 to end of August 2007. It is well-known that the mean temperatures during winter periods are smaller than those of summer periods. Our aim is to test whether there is also a significant difference in the autocovariance structure of the winter and summer periods. The data consists of two samples of curves $\{(X_{t}, Y_t),\;t=1,2,\ldots, 92\}$, where $X_{t}$ represents the temperature of day $t$ for Dec2006-Jan2007-Feb2007-March2007 and $Y_t$ for Jun2007-Jul2007-Aug2007. More precisely, $X_{1}$ represents the temperature of the 1st of December 2006 and $X_{92}$ the temperature of the 2nd of March 2007, whereas $Y_{1}$ represents the temperature of the 1st of June 2007 and $Y_{92}$ the temperature of the 31st of August 2007. The temperature recordings were taken in $15$ minutes intervals, i.e., there are $k=96$ temperature measurements for each day for a total of $T=92$ days in both groups. These measurements were transformed into functional objects using the Fourier basis with 21 basis functions. All curves were rescaled in order to be defined in the unit interval. Figure \[fig:win-sum\] shows the centered temperatures curves 