Have a odd starting issue with a customers 2003 STX-12f.

When its 60-ish degrees and warmer outside the machine starts up perfectly within 2 seconds of hitting start button and runs/idles perfect.

When outside temp is below 60 degrees it takes the machine about 40 seconds of cranking before it will start to sputter and eventually start.

(starting fluid sprayed into aitbox will make it start immediately no matter what the outside temperature is)

Once warmed up it will re-start perfect every time.

Besides the cold starting issue the machine revs out and idles like new(Does not die at idle or when let off the throttle fast)

I dont think the throttle body is the issue

Could it be failed exhaust temperature sensor or oil temperature sensor? I read one thread where a guy said he replaced both of his and it fixed the cold starting issue but figured Id ask on here to see if thats a known issue?