Background
I live in an apartment. Each room is heated by a radiator controlled
by a knob that apparently opens & closes the valve to the radiator.
The apartment does not have a thermostat.

As a result of the absence of a thermostat, I frequently have to turn
the radiator knobs. Even so, my apartment is often over-heated and
under-heated.

The management of the complex (a co-op) is unwilling to install
thermostats in the apartments due to the expense.

Question
Can I install thermostat(s) in my apartment? How do I know which one
to buy and from whom to buy it.

There are such things as radiator thermostats.  I can't answer whether
it's legal or you have the skill needed to install one.  This page
says you should hire a plumber to do it (cell D8):

http://portal.est.org.uk/uploads/documents/partnership/Explanatory%20text%20for%20recommendations.xls

In case you don't have Excel, the relevant passage says "You will need
a plumber to fit them to every radiator except one - the radiator in
the same room as your room thermostat."

I'd say first find out if it's legal according to the terms of your
deal with the building (I'm not familiar with co-ops), and if it is,
hire a plumber, who will be able to advise you on selection.