higher engine temparature at day ?

Having the AC on does produce some more heat in the AC radiator, so the normal radiator may not cool as well. This isn’t a serious problem as long as the temp only goes up slightly.

BUT, please don’t use plain water as a coolant in a modern engine. Reason is that “anti-freeze” is only one of the functions of the coolant mix. It’s also a Corrosion Inhibitor. Plain water actually works fine as a coolant, and you can use it in an emergency. But you will have galvanic corrosion starting between the different metal alloys inside the engine and cooling system. This eats away at the engine from the inside, and plugs the cooling system with the rust and aluminium oxide. Eventually the engine is ruined.

Big shot with an LS2 can’t scrape up $20 for engine coolant? The POSEUR alarm is going off, loudly.

You will wreck your engine using strait water, not coolant. It has stuff in it to protect the interior of the engine. It is not unusual for en engine to run a bit higher when A/C is running.

Temperature increasing with the A/C on or in the heat of the day is a good sign of a slightly plugged radiator. Using tap water instead of coolant diluted with deionized or purified water will do that. If the radiator is working properly it will expel all the heat necessary regardless of the heat of the day or added heat load from the A/C. My top suspect for the water loss is the radiator cap, only because it is a pressure-holding part that cares how warm the engine is running. A visual inspection of the rubber seals on it, especially the outer seal, will tell the story. Cracks mean time to replace.

There is not practical way to repair a radiator that is being plugged by hard water deposits. The lower tubes are plugged solid with limestone. I tried CLR on a radiator with that sort of plugs and it fizzed impressively but made no visible difference in the stony deposits. If the running higher than usual graduates to beginning to overheat the radiator will have to be replaced.

The LS2 engine was introduced in 2005, when the intake manifold gaskets were finally made compatible with Dexcool. This is a good time to drain the cooling system and switch to Dexcool prediluted or diluted with purified water. It sounds like you are keeping close enough watch on it to avoid the low coolant levels associated with Dexcool sludge.

You should always use 50% antifreeze+water mix, never just plain water, otherwise all the different metals and gaskets in the engine will corrode and plug up the cooling system, which could cause overheating. Check the rubber hoses for pinholes and hose clamps for tightness, which could cause coolant leaks. If the hoses are OK, try Bar’s Leaks liquid (NOT the pellet version), which might seal a tiny leak.