that booster hose is just one of may hoses, to pinch and block to find vacuum leaks on all cars.
Pinch test #7 here
http://www.fixkick.com/IDLE-AIR/leaks/Hi...-List.html
Thermostats fail in many ways, (like starters) the STAT be very very slow to open or open to fast and too far.
in fact, there is netflix video on "how Stats are made" and why they fail and why they all fail so soon.
the wax pellet inside, is short lived. as are some seals inside, what cause the motion of the STAT, all fail soon, not one lasts life of engine.
running with no thermostat is one of the worst things to do with EFI.
the EFI is now locked in warmup mode forever. waste of fuel and a very hot CAT.
the engine actually, cools better with a
195F stat, (seems odd huh?) but do to "Carnot's" laws .seen here.
http://www.fixkick.com/overheating.html
the radiator has greater cooling effect, with water more hot, than the air side. all auto stores sell this stat,
http://en.wikipedia.org/wiki/Carnot%27s_...ynamics%29
and better MPG.
when replacing the STAT with wrong gasket,(ring) clauses a fridge engine.
see TSB warnings here from suzuki on this topic/
got a 4mm Stat rim or 1 MM? (in the intake stat pit)
http://www.fixkick.com/Cooling-engine/Fr...r-cab.html