User suspensions are between Stack Exchange and the user only. They are accompanied with an "Private Message" detailing all the reasons as to why they are suspended. This is not shared publicly in order to protect the interests of the user. You can read more about it in this elaborate meta post Why we don't keep public records of suspensions
This is the 2nd suspension for him with hardly 2 days have elapsed after his 1st ban ended.
Some stuff which are taken rather seriously after one suspension. When an user gets back to doing the same act for which they have been suspended, they would usually get a longer suspension term. (There have been instances of users getting banned for an year, more than 2 times).
I want to know what led to his 2nd temporary suspension?
This, as I mentioned in the introduction, is private to that user. We can get to know some reasons by looking at the suspension reason. Here it is "to cool down" which implies that the user has engaged in some disruptive behavior which is against the code of conduct of Stack Exchange..
Will an user getting repeatedly temporary bans be banned permanently after few such occasions?
There are no permanent bans on the site. An user can come back, repeat the same act and get back into another temporary ban within a few seconds. See A Day in the Penalty Box.
By, Permanent bans, if you mean account deletions, then they are usually reserved for outright trolls who disrupt the functioning of the site. You usually won't find these on smaller sites like ours. (I can give one example from Stack Overflow)
Is it the local moderation team that bans or the CM team? if the later, then how do they know that they have an user to ban? Does the local moderation team prompt them in some ways?
Either of them can ban an user. Infact any one with a ♦ next to their name can suspend a user. (Community included). Usually the CM team won't step in to ban a particular user unless the moderator team have explicitly approached the CM team. Another reason where the CMs would ban an user is when they are contacted directly through the /contact page about the activities of a particular user, and they determine that it is ban worthy. (CMs are usually too busy to handle the suspensions of users on site).
Network bans are administered by CMs. If a user has been disrupting on more than one site, (like a child meta and the main meta), a CM can choose to suspend that user network wide.
i don't agree with the rule that the reasons for suspension can not be investigated upon.
The reasons for suspension can be investigated upon, but just not by us. The particular user who has been suspended has a few ways to contest their suspension.
To reply to the moderator private message and mention their arguments against the suspension.
To contact Stack Exchange and inform them of moderator foul play.
Remember that suspensions and private messages are taken quite seriously and any moderator who is found to have sent an unwarranted moderator message (with an ulterior motive) would be removed immediately from the moderator team.
Are new users dealt with any differently from relatively old users as far as taking ban decisions are concerned?
It is not the duration for which the user has been there on the site that counts but it is the amount of valuable contributions that the user has made to the site. An user who was created 2 years ago, but added a spam answer yesterday would be "destroy"ed immediately, whereas a new user who has a few other good answers, but added a nonsensical answer (pure gibberish) would just be suspended.
Similarly, when it comes to the timed suspensions, there is no difference made between new users or old users. (The duration of the suspension depends upon the impact of their action and their past history). For example, if a 20k rep user were to go around leaving abusive comments on the posts, they would be suspended. The same would be the case when a 1 rep user does it.
If the suspended user creates new accounts to surpass the ban and participate on the site with new account, the new accounts will be deleted and merged and the suspension period may get extended because creating sock puppets is another violation.