I have just learnt that in C language malloc function comes with the issue of thread contention when used in a multi-threaded applications.
In C++ does operator new suffer from the same problem? If yes what tecnhique can I use to avoid this that sounds like a big penalty in the application performance?
That "issue" of thread contention really depends on the implementation. Some of the implementations of malloc in common use were not originally designed with multithreading in mind. But a malloc implementation designed for multithreaded applications shouldn't suffer from contention in normal circumstances.
As an example of a malloc implementation designed with multithreading in mind, look at jemalloc.