97 Cobra cooling Problems!!!!HELP

My newest Rio Red 97 Cobra has had some cooling problems since I bought it. I went to go install a 160* stat and when I installed it, I noticed the previous owner wasnt running a thermostat. I put it in and it was great for a while then it started running real hot after a week. The temp guage was reading on the L in "NORMAL." Then I saw a thread saying you shouldnt run a thermostat under 180* because your computer wont like it and it will always run hot. When I had the 160 stat in it ran on the L for like 5 minutes, then it would cool down and run halfway and below. I didnt like that. So today I bought and installed a 180degree thermostat and the same thing. It gets real hot,on the L for 5 minutes then finally starts cooling down and running fine. Is this safe?? It shure doesn't seem like it. It seems like something takes too long to kick in, then it finally does. I thought at first it was the 160 thermostat, but its doing it with the 180. Need advice. Is it the Fan, the Radiator? Is there something else Im missing?
 
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