05 running hot need advice

[JParisi48]

I just bought this bike used. It runs great idles great everything. By the looks of the exhaust coloring it's not running lean, maybe a tad rich it's darker in color not a light grey. Idk if it's a problem or not but the cylinder gets warm within not even 30seconds of starting it. It warms up very fast. I. Had a kfx before and it took minutes to warm up. Is this an issue? When you start your bike and let it idle how long before the cylinder is warm? Has full coolant fresh oil everything I can think of

[LxMxL97]

I just bought this bike used. It runs great idles great everything. By the looks of the exhaust coloring it's not running lean, maybe a tad rich it's darker in color not a light grey. Idk if it's a problem or not but the cylinder gets warm within not even 30seconds of starting it. It warms up very fast. I. Had a kfx before and it took minutes to warm up. Is this an issue? When you start your bike and let it idle how long before the cylinder is warm? Has full coolant fresh oil everything I can think of

Does the temp light come on?

[JParisi48]

No but I'm not even sure if it works.

[LxMxL97]

No but I'm not even sure if it works.

It should come on for the first 5 or so sec when you first start your bike