A GT 1030 only draws around 30 watts of power from the PSU, so it will likely work, as the rest of your components are probably not drawing too much more than 100 watts from the PSU under load. I've even heard of people successfully running something like a low-profile GTX 1050 in these 240 watt small form-factor systems, though those can draw closer to 70 watts under load, and may potentially push the PSU close to its limits.
As a suggestion if you go with a GT 1030, make sure you get one with GDDR5 memory (like the one linked to above), not one with DDR4, as those will tend to be notably slower.
As for the fan, it's difficult to say, since they sometimes use a larger heatsink to make up for the lack of a fan. The fan versions will probably run a bit cooler more often than not though, particularly if there isn't much air circulating around the card.