It depends upon the size of the air line coming into the equipment and the exhaust of the air from the panel, the line pressure, the low pressure setpoint, etc..

Suck it and see.

Or,stick a dedicated panel cooler on it and forget the problem.

Use a water/coil type if chilled water is available,alternatively use a self contained refrigerant type.There are extreme ambient versions available.

Run your vortex tube cold air through a coil of copper tubing that is inside the panel enclosure. Seal the tubing entrance and exit, letting it exhaust outside the enclosure. Cooling will be by convection between the air in the panel and the tubing. The panel can keep it's pressure constant.

If the line can take the intermittent swiched flow of air to the Vortex tube without much pressure surges, it may be ok. You can try adding a buffer chamber to the vortex inlet, which may minimize this effect.

It sounds like you need a seperate air line for the Vortex ?

I do not think its a great design to use your instrument air which is a interlock for your normal plant operations for cooling purposes, even if you are using that why is the back pressure regulator not installed to ensure that the pressure fall is limited to above your interlock value, The regulator will always take a feedback from the line pressure before the regulator and maintain the pressure.

Best remove this inst air line , if it is harsh and cold place a thermostat and a heater arrngement and a panel cooler. That shoild take care,

Your situation is same as we were having before. We also've an outdoor panel containing SCADA in industrial PC, PLC, many electronic cards & electronics in it. The temperature of the panel was too high and our PC was always getting hanged due to high temperatures.

So to avoid it we'd installed a panel A/C and now all of our problems are solved.

I guess you've got your solution.

The best and economical sensible cooling of the panel is with air/water cooler used in desert. A portable paded air cooler feeding air from bottom of the panel to be exhausted from top across by a minature panel fan.