This study investigates the relationship between particulate matter that have an aerodynamic diameter less than 10 µm diameter (PM10) and air temperature (T) in the Caribbean basin. To conduct this analysis, eleven years of daily time series recorded in Guadeloupe archipelago were used. Firstly, the stationarity threshold of both time series is quantified using the infinite moving average. Then, statistical analyses were performed using the conditional mean and the joint probability density function method. Both methods used showed a dependence between PM10 and T particularly during the high dust season, i.e. from May to September. From a dynamical point of view, the coherence function highlighted a global correlation information between PM10 and T in the frequency domain. To capture possible localized correlation information, both time series are studied in a multiscale way using a new cross-correlation technique classically based on Empirical Mode Decomposition (EMD) termed the Time-Dependent Intrinsic Correlation (TDIC) analysis. After computing EMD and Ensemble Empirical Mode Decomposition (EEMD) methods, a mode-mixing problem is detected in EMD frame. Consequently, for the first time in air pollution field, a combination of EEMD and TDIC is performed. The achieved results show that the strength and nature of association between PM10 and T vary with time scales and time spells. We found that PM10 from African and marine aerosols are strongly correlated to T respectively for large and small periodicities. One also observed that extreme weather events such as heavy rainfall, hurricanes or drought induce a strong anti-correlation.