Perch can handle almost any condition present in most lakes and ponds in North America, but they are forced to follow their forage and stay in those areas because this prey has a more finite set of habitat requirements... For trout and salmon, they absolutely require higher oxygen concentrations and cleaner water. For some fish species, their main food source dictates where they will thrive, while other species survive in a set range of conditions and these must be present for a successful, sustainable population to exist. These are just examples, hopefully I've helped explain something about this subject (fish biology).
As far as a thermometer, I'd say that mid to late winter would be the best time to use it because of the depleted oxygen levels in the water