Are they safe to leave unattended and do you think it’s ok in a tight space with paints/flammable liquids/etc?
It depends partly on the flammability of the liquids. Highly flammable liquids will produce flammable vapours at lower temperatures, and if the containers are in a confined space with little or no ventilation, then there might be a risk of a flammable concentration of vapour developing as a result of a leak or a not very tight fitting lid etc., which could then be ignited. Highly flammable liquids would include thinners, and possibly some paints and glues.
The issue with electrical heating – or other electrical apparatus – and flammable vapours is mainly the potential for a spark (the surface temperature of the heating element can sometimes also be an issue, but I doubt it’s relevant here for the sort of trace heating to which maccruiskeen is referring). The point at which sparks occur in electrical circuits is the switch, so it might be OK if you positioned the switch for your trace heating element outside the box (this is how bulk flammable liquids storerooms are usually arranged: the electrical components inside are of a very expensive type that will not ignite flammable vapours due to their design or special enclosure, but the switches for the lighting circuit are positioned outside the room to allow ordinary cheap light switches to be used). That still leaves the risk of things like damage to the circuit resulting in a spark, something to which a trace heating element might be vulnerable if it was not protected against knocks and impacts.
You could install a thermostat inside so that if cuts off at anything more than a few degrees above zero
Since a thermostat is a switch, I would not do that for the reasons described above.
Frankly, it sounds more trouble than it’s worth: you have to build the container and install the heater, you have to remember to switch it on in winter when it gets cold, you have to remember to switch it off when not needed. If the heater develops a fault it might not be apparent until you find your paints and glues are again ruined.
Dont bother making a box, there’s always people trying to get rid of old fridge freezers
That sounds like a much better idea. It’s possible you might not even need any form of heating. You could put a cheap thermometer inside it, maybe even the type that records high and low temperatures, and see if the temperature inside it the freezer was falling too low in the event of a prolonged cold spell. In an emergency, you could heat it temporarily by sticking a brick or two in your oven after cooking a meal, and then transferring the warm/hot brick to the freezer.