Tm of DNA depends on a fine balance between hydrogen bonds between bases, hydrogen bonds between bases and surrounding water molecules, and base-stacking interactions between adjacent bases. High DNA concentration favors duplex formation hence the Tm increases.
DNA melting point does not depend on its concentration. Instead, it depends on its length, base compositions and ionic strength [salt] of the solution. For instance, Tm of a 20-bp DNA solution at 1 mM or 1 uM is the same in identical solution conditions.
Since DNA hybridization has a cooperative effect, the number of DNA molecules will dictate the probability of the complementary base pairing. Consider a sub-volume of let's say 1 nl. Now, imagine you have two cases: A) 100 DNA molecules or B) 10.000 DNA molecules in such a volume. The probability of re-hybridization is higher in case B). That's why, for example, the melting curves are significantly different when DNA hybridization takes place on a microarray!