Doc Murray -- My Undies Are Clean ... and I'm Thrilled!

Conrad Murray's prayers have been answered -- the good doc got a fresh pair of underwear and a clean jail uniform this week after lodging major complaints about the way he's being treated behind bars.

TMZ broke the story ... Murray believed he was going to die in L.A. County Jail ... claiming he's being treated like filth -- getting fresh air once a month, and fresh underwear once a WEEK.

But after lodging his complaints, we're told Murray saw immediate results. In fact, Connie told his lawyers a swarm of deputies came into his cell Monday morning ... and couldn't have been more accommodating.

Besides the clean clothes, Murray got a new blanket ... and was taken to the roof so he could get some fresh air.

A rep for the L.A. County Sheriff's Dept. tells us Murray is receiving the appropriate level of care for the headache he was complaining about. The rep also claims Murray was evaluated by a doctor last week.