Be careful if you opt to simply replace the temp sender - all too easy to get a mismatch now. There was originally a dealer recall on some early models where the gauge was scaring owners and they swapped in a matched pair sender and gauge that read a bit lower and acted differently so as to reduce concern. Not sure there are too many different choices if you buy a new sender today, so you could risk having one that incorrectly reads high/misbehaves, or just as easily gett one that is spot on. Another reason to work with an IR temp gun so you work on actionable data, etc.
I'd would simply make sure the push-on connector is clean/shiny, no corrosion on it or the sender stem, then gently squeeze it a tiny bit so it firmly grabs and holds onto the stem when connected. Don't forget to add a bit of connector grease/dielectric paste. If the connector is damaged/badly corroded, buy a new one and splice it on.
I'd would simply make sure the push-on connector is clean/shiny, no corrosion on it or the sender stem, then gently squeeze it a tiny bit so it firmly grabs and holds onto the stem when connected. Don't forget to add a bit of connector grease/dielectric paste. If the connector is damaged/badly corroded, buy a new one and splice it on.