Does the hose need replaced, or is something else the culprit?

Hello again all!
I have been diligantly working on the suggestions (any newcommers please don't hesitate to check out my other topics*mainly about a
tapping noise, and horrible gas milage W/ high idle- I'll take all the help I can get :)
NOW the new one.... I have noticed, during a vacum line inspection (of
which was unseccessful- sounds like the whistle is coming form right by
the drivers-side firewall... somewhere... so hard to follow a whistle!)
anyhow, I noticed a "blown up" tube attached just below my T-stat housing. Not the big hose from the radiator ON the T-stat... a small hose, it's not leaking, but it's blown up like a small ballon- which can't be good. I'm not sure what hose this is... could it mean the T-stat is stuck closed (but it seems to me it can't be cause my temp fluxuates and the hose on the radiator acts like it is opened when it's getting warm.
Thanks for any and all help!

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