Is it allowed to work when holding a temporary resident visa?

You will need to head to your local SRI and apply for a RUC under your passport number

SRI will explain what if any filing requirements you or your employer has for your employment or business and what benefits you are owed, what your minimum wage is and what deductions you are entitled to for your work.

Is it legal to work under temporary resident visa?

Yes, however you must register yourself or be registered through your employer.

By the way, you may have to wait a bit for things to shake down as temporary resident is a new "thing" here. Previously we had tourist which was non resident and resident visas.

Since a tourist required a tourist work visa, a different animal from what you are asking, now recently extinct, many will assume that's what you are inquiring about.

Well, yes, it's new and quite uncertain yet. What I applied is the 9V professional Permanent Resident Visa late last year, however, as new law came into existence, the application I think has become a 2 year temporary resident visa. So I think the "resident type of tourist requests a work visa" type isn't my condition. However the time is quite embarrassing here because I am considering to have the visa done in Ecuador, so I really need to make a decision ASAP, but still afraid of any changes or uncertainties. Otherwise, I can wait and see what it would become.