There is no specific temperature at which the ECM clicks over to closed loop. It's a combination of things, most important of which is actually the exhaust temp. Once the O2 sensors reach 700 degrees, they start switching, and the ECM sees that and says to itself, "hey man, I sould be doing something here". It then checks the ECT to see what the temp is this side of the radiator, and if it has reached 150 degrees, it
may go into closed loop. It also may not. As a rule, the ECM should go into closed loop long before the t-stat ever opens, but it depends on several other sensors, and the info they have to share. If you were to substitute a 160 t-stat in place of the OEM 192 t-stat, the ECM would still go into closed loop, but as soon as it got used to the fact that the temp changed so early, subsequent start ups would be much more unstable. The ECM knows specific ranges of ohms and volts, and when some sensors are withing the range they are supposed to be, yet others are not, the ECM decides that something is wrong, and reverts to another preprogrammed set of parameters, and acts accordingly. The end result will be a car that feels peppier at first, but quickly becomes sluggish, and eventually dies because of clogged cats and diluted oil.
Sorry, there is no cut and dry specific answer to your question. I spent 2 years, and a million resources, learning that.
Take care,
-Chris