+1...but don't just worry, you do have to do something.
Therm broken closed, the car would've stayed overheated.
WP failing could explain that...the greater speed while moving would circulate coolant, while idling, not enough...so look for leaks and listen to WP for wonkiness.
A broken fan would also do this.
Look for leaks when you are home...turn car off it temp rises above dead center.
Could just be temp sensor, but don't chance it OP...simplest thing to diy is just a whole cooling system overhaul...about $300 in parts and easy diy with lots of help here.
Or, pay $300 and maybe get the one component you actually need replaced by an indy.
But, working with all new parts, you'll undoubtedly get the part that's broken fixed...unless it is the fan...and that you should check definitely...again, many threads on this...if auto, might just be fan clutch...but having a manual, I don't know what else might be there beyond a fuse (check) and maybe a relay (check).
I'll say it just to emphasize what Orient said correctly...next step in ignoring overheating engine...head gasket $12-1500....add a head for another $1000, or more seriously screw up engine and buy a new engine...costs more.
I cracked a head in my e36...and then started learning all I could so I wouldn't do something stupid again...didn't work...not even close...but my car is pretty well maintained!
HTH
Doug