It took a long time for the connection between body temperature and illness to be made.It作什么成分?connection作什么成分?to be made作什么成分?

it在这里是形式主语， connection是作为宾语的， to be made在这句话里是真正的主语。
实际语句可以是：To make the connection between body temperature and illness would take a long time.

for the connection between body temperature and illness to be made.
这个整体是介词短语作状语，对...来说。connection当然是做介词for的宾语。
to be made是不定式的被动式做illness的后置定语。
至于It 是主语，作无人称动词的主语,表示时间、气候、距离等
这里不应该看成形式主语，因为句中无真正主语成份。

It作形式主语，connection作宾语， to be made作真正主语。
between body temperature and illness 是宾补

It作形式主语，connection作宾语， to be made作真正主语。

it 是形式主语 connection是主语的一部分,the connection between body temperature and illness to be made做主语,to be made做目的状语