We want to characterize the properties of the cold dust clumps in the Carina Nebula Complex (CNC), which shows a very high level of massive star feedback. We derive the Clump Mass Function (ClMF), explore the reliability of different clump extraction algorithms, and investigate the influence of the temperatures within the clouds on the resulting shape of the ClMF. We analyze a 1.25x1.25 deg^2 wide-field sub-mm map obtained with LABOCA (APEX), which provides the first spatially complete survey of the clouds in the CNC. We use the three clump-finding algorithms CLUMPFIND (CF), GAUSSCLUMPS (GC) and SExtractor (SE) to identify individual clumps and determine their total fluxes. In addition to assuming a common `typical temperature for all clouds, we also employ an empirical relation between cloud column densities and temperature to determine an estimate of the individual clump temperatures, and use this to determine individual clump masses. While the ClMF based on the CF extraction is very well described by a power-law, the ClMFs based on GC and SE are better represented by a log-normal distribution. We also find that the use of individual clump temperatures leads to a shallower ClMF slope than the assumption of a common temperature (e.g. 20 K) of all clumps. The power-law of dN/dM propto M^-1.95 we find for the CF sample is in good agreement with ClMF slopes found in previous studies of other regions. The dependence of the ClMF shape (power-law vs. log-normal distribution) on the employed extraction method suggests that observational determinations of the ClMF shape yields only very limited information about the true structure of the cloud. Interpretations of log-normal ClMF shape as a signature of turbulent pre-stellar clouds vs. power-law ClMFs as a signature of star-forming clouds may be taken with caution for a single extraction algorithm without additional information.
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