S-10 Slow to start when warm
 

I have a 99 s-10 LS with 100k .
I have recently changed oil , oil filter , fuel filter,air filter, plugs , wires, and battery. First thing in the morning the truck fires right up like brand new.After its warmed up then stopped (i.e. parked and shut off to run into the store) it is very sluggish to start up, sometimes it takes two attempts. Once it sputters to life it runs great no idle issues or stalling. I have heard the coolant temperature sensor could be an issue and fits some of the symptoms I'm experiencing , however I'm also told that this model has only a sensor and not a sender ( to the temp. gauge in the dash.) and a sensor (to the computer) My question is if my temp. gauge is functioning is it worth the time and $ to attempt to replace the sensor ?

post a video thanks