You could get some electrical tape and just cover it with enough layers to cover it all and keep it secure, but it may need replacing every so often due to it losing its stickiness.
You could also get some shrink wrap, and if you ahve something that outputs around 80c heat constantly then you can cut the shrink wrap into 1 long piece instead of a cable-like figure, and wrap it around, and melt/shrink it over the exposed cable. This is probably the best option for long-term durability.