My 2003 s-10 is starting rough only some of the time, and runs fine after an initial hiccup. After several hours of operation starting becomes increasingly difficult and it started to get above normal operating temp., yet ran for hours at the correct temp. the next day. I just replaced the radiator and change from water only and bars leak sludge to a dexcool, water and minor sludge in there now. I got oil change used seafoam treatment, cleaned k+n air filter

Are you talking about a go-cart, or a motorcycle, or a tractor-trailer 18 wheeler? Then OF COURSE, you must IDENTIFY the MAKE, the MODEL, and the YEAR of whatever vehicle you are asking about, if you want any REAL help!

Does this problem become more common during cold weather days ? Or when it has rained ? Humidity and moisture can affect a few components which make it hard to start.

Might want to double check your vacuum lines also.

I would ck the cooling system, sensor, head gasket etc. Is any oil getting in the coolant or visa versa?

Well the starter won't cause the rough running or stalling problems.
You would need to know if the starter has full battery power when it will not crank without being jumped off another battery.
It could be that the battery voltage drops low enough to affect the computer memory, and after the engine starts the computer has to re-learn the settings.

Check the fuel filter,or just change it,it is more likely it is stopped up.

Check the primary and secondary resistance on your coil and resistance and gap on your spark plugs. Sounds like you have a high temp foul out.

your choke is sticking

replace the accalerator pump in the carbrator this is located at the bottom of carb. or front above fuel filter! this should cure the hiccups and problem.

I found the fuel pressure regulator on the fuel rail was leaking fuel into the intake manifold via the vacuum hose.Was hard to start and rough idle. Pull vacuum line and see if fuel is coming out-if so like me-replace it. About 50.00 at Murrays. Also the two inner cylinders on the passenger side-opposite of the vacuum line will be very rich fouled-replace them all

Could be vacuum leak or bad ignition wire(s).

I had a similar problem on my "93 Ford probe. The engine idled pretty rough with shakes, Turned out to be a head gasket leaking engine coolant into the cylinder during low rpm's. At fast rpm's it was fine becuase the internal cylinder pressure was greater than the hot coolant pressure & would prevent the coolant from leaking in.

A friend has the same problem with his "94 Blazer 4.3 L, throttle body injection, manual tranny. He hasn't fixed it yet, It started a few weeks ago & is getting worse. His gets a fast idle with hiccups which causes the engine shake. He already checked the EGR valve. He also has a severe exhaust problem, Not oilly but very gray & terrible smelly, but only when the fast idle problem happens. THis fast idle hiccup problem starts when the engine is warmed up.