0.05°C is about 0.1°F, I held temperature that tight for paints/sealers/adhesives and the like during a previous employment. Properly tuned PID controls for solid state heating relays, and pulsed chiller loop feed, properly sized for flow & surface area. 0.5°F/.25°C for most jobs that didn't need tighter control was fairly easy.
I'd imagine if the exchanger and temperature sensor contact surfaces were made of a thermally conductive metal that was rated for service in the acid you'd be able to control it. Keeping the acid agitated to provide even control would be the more difficult aspect, depending on the geometry of the tub, relative volume, etc.