If length is the issue, one of the single fan models should fit. If height is the issue you'll need a low profile card. If you can't find a low profile 1060 then maybe a 1050 Ti will do.
I don't think overheating will be an issue but I do think it's possible any gaming card you use will run hotter than in a more air flow friendly case. This is not bad, but the downside is this might mean more fan noise. I'm sure the fan will keep the card in safe temps, it'll just have to run faster and therefore make more noise.
Check things like the power/reset button connector. If the motherboard is non standard the first clue will be unusual connectors, such as for the power button.