Should I still look for other work if I accepted a temp-to-hire position?

Hi, everyone. I finally received a job offer after being unemployed for over 3 months now. It’s been difficult to find a job but I’ve finally found a decent place. It’s a big company but the office I’ll be working at is very small and quiet, decent driving distance (about 20 minutes away), set schedule, and higher pay than my previous job which is $1 more an hour.

I’m definitely accepting because I think my short length of experience is the reason why it has been difficult to get a job in HR. The thing is, this is only a temp-to-hire position. Anywhere from 4–12 months they can take to decide whether they want me permanently or not. No benefits…NOTHING. I was hoping for benefits too because of some health conditions I have…
I’m afraid they can take advantage and wait ONE year before they want to hire me on completely.

Anyways, should I still look for other work and be interviewing just in case? I’ve never had a temporary position before so I’m not sure how it works. If they don’t want you, is it considered being FIRED?

Thanks!