Currently I am working on a project which requires 1000s of temporary valid and unique email addresses for bulk sign-up process.

Solution
Currently there are several on-line temporary email account provider available. The one I was using till date is http://mytrashmail.com/ , there are other too. Problem with these services is you would not get mail to these temporary email accounts cent percent time.

Best solution
Fortunately Google solved this problem few years back by providing some customizations on their email. So, using your Gmail email address you can create any number of email ids and for each email id mail would reach to your Gmail account only. In other words you can create any number of aliases of your Gmail id and all aliases would point to same account which is main account.How to create Gmail email address aliases
Lets assume my gmail address is manish@gmail.com then aliases of this mail id would be manish+<ANY WORD>@gmail.com e.g., manish+test1@gmail.com, manish+test2@gmail.com, manish+test3@gmail.com, manish+test4@gmail.comIn the above example I have replaced <ANY WORD> with test1 or test2 or test3 etc. You can place anything instead.