Do you have a chiller or just a fan cooler? Chiller will have a LED display with the +/- temperature on it, or an error code. Fan cooler is just a square box with a fan and some coils in it. Fan cooler machines will get hot after a while. Pumps impart more heat into the water than machining, so if you have just the filter pumps running for a long time but no tank circulation, there is no water flowing through the chiller, and the water will get hot. Or, your chiller has simply failed.
Filters are critical. Skimping on filters just transfers the work to your DI resin. There is no free lunch. Filters pull out particles down to the 3-5 micron range. DI bottles remove the remainder and any dissolved solids. It is those solids (ie, metal debris from the EDM process) that cause the water conductivity to rise, so one way or another, those particles will be getting removed, but it's far cheaper to let the filters do that work than the DI bottles. Filters need to be changed out every couple hundred hours or so, give or take, depending on the type of cutting you are doing, the material you are cutting, and the quality of the filter. Don't trust the pressure gauge for the filters alone, if they have clogged then internally cracked the pressure will be low, but only because the water is all leaking out of a hole and no filtration is happening (bypass). Often a cracked filter will have "squirters" or streams of water shooting out of the sides like a water gun against the filter cover. If you see these, the filters are bad and need to be changed immediately. DI bottles/socks must be replaced when the conductivity level no longer remains under 2.5 (or 25, depending on the era of the machine; some don't show the decimal).
So what is the effect of bypassing the probe and letting the conductivity levels rise? Poor finish, wire breakage, unstable cutting, increased wear on power feeders, increased contamination in the work tank, unreliable threading (due to contact sensors in the AF system falsely detecting wire thread complete), possible contact alarm with wire on, control not detecting VG properly thus affecting cutting speed and tolerance, etc, etc, etc.