Help with radiator/thermostat issue for my 65 Dart?

HI there - need some insight into a weird thing that happened to me last night. I just acquired another 65 Dart (my previous one stolen) and last night around 8pm I drove her down the street to pick up something....a few blocks down and back. I noticed when I pulled into my parking spot the temp gauge was all the way up. (The guy I bought her from said this sometimes happens - where it kinda fluctuates up and then back down)when I shut off the car I started hearing a bunch of liquid hitting the pavement. I get out and there's a good steady stream of radiator fluid coming out! I opened the hood and it appeared to be coming from the overflow hose? (I did not have this hose on my previous Dart - at least not that I noticed). Today I added some water to top it up, started it up for a few minutes, and don't see anything amiss. No leaks anywhere. A couple people mentioned that it might be the thermostat? I'm calling my mechanic on Monday but am hoping for any insight before then.

thank you so much!

(photo of overflow hose attached)

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