Ok, this is starting to get all confused up. Lets use words for the TLA's. ( three letter acronyms )

CHT = Cylinder Head Temperature. Mine runs in the 235'F to 240'F range.
CAT = Catalyist temperature. Mine runs in the 1300'F to 1500'F range.

So far, I've had EV at Catalyist temperatures of 750'F or warmer.
( which is basically always )
I do not have any clear correlation to CAT temp and EV operation.
Before the new ScanGauge, we all thought there would be, but maybe we were all wrong. The CAT temp is not measured anyway, it is just an inferred value... a "best guess" based on other factors.

Now, there is FOR SURE a correlation to Water Temp, CHT, and EV.

In 2005-2007, the REQUIRED water temp to enter EV is 140'F.
I AM POSITIVE OF THIS! This is set in STONE. ( or iron. )

In 2008's, I hear from owners this requirement is higher, but I've not seen it for myself.

Once in EV, you can continue to use EV down to Water Temp. 125'F.
In almost 3 years, my car has never violated this rule.

But this is not the only requirement.

ALSO... the CHT needs to meet minimums at the same time.
And here is where I find the rules change, based on weather.

In BELOW FREEZING weather, you need 140'F water and CHT 224'F at the same time to enter EV.

In BELOW FREEZING weather, you can stay EV down to water temp. 125'F and CHT 202'F. Whichever crosses the threshold first will trip the engine back on.

In above freezing weather, my 2005 changes the rule for CHT but not water temp. In above freezing I have had EV with CHT down to 177'F.
But my car never ever breaks the water temp. "rule".

Hope that helps.
-John