How to tune update using subquery

Question

T1 has 4 million records
T2 has 9 million records
Average number of records updated in T1 = 115,000
I am trying update table T1 (4 million records), with matching t_id from table T2 (9 million records), every night.
I tried the 3 version of the update, each of it taking around 30 minutes to update T1.
If I run the same sql immediately it completes within 5 minutes (execution plans are the same for both runs).
Could any one please explain what makes it run faster the second time? Any suggestions for performing this
update in a better way would be greatly appreciated...
create table T1
id varchar2 (18) not null,
t_date date not null,
t_id varchar2 (18),
processed varchar2 (1) default 'N',
constraint T1_pk primary key ( id, t_date )
create index T1_prcsd on T1(processed);
create table T2
id varchar2 (18) not null,
t_id varchar2 (18) not null
create unique index customer_idx01 on customer(custnum);
**1:**
update T1 a
set t_id = ( select b.t_id
from T2 b
where a.id = b.id)
where id in ( select id from T2)
and processed = 'N';
*2:*
update T1 a
set t_id = ( select b.t_id
from T2 b
where a.id = b.id)
where exists ( select 1 from T2 c where a.id = c.id)
and processed = 'N';
*3:*
update ( select /*+ USE_NL(T1) INDEX( T2 T2_idx01 ) */
                              a.t_id a_t_id
                              ,c.t_id c_t_id
               from T1 a, T2 c
               where a.id = c.id
               and a.processed = 'N'
set a_t_id = c_t_id;

Answer 1

Could any one please explain what makes it run faster the second time?Probably because data is cached if the second run is shortly after the first.
You already tried the correlated EXISTS I was going to suggest. How long do versions 1 and 2 take?
Are A.ID and A.PROCESSED both in one composite index?