To be safe you should turn the pilot light out until the paint is dry and run a fan before you light it to be sure no fumes are left in the area.

Use latex paint - you won't have a problem - it isn't flammable...

Mr. Paint

What MR.Paint said is true,latex will not and cannot ignite.
If you using oil based yes shut it down to be on the safe side.

What about spray paint near gag hot water heater?