The higher the tempco, the more they will change with a given change in temperature, so you're looking for low tempco parts.
Some of the best are the metal foil resistors, and some of the cheapest thick film/carbon resistors are some of the worst, but there are a bunch of fairly inexpensive intermediate types which could fit the bill depending on what you need. In your case though, the tempcos are in ppm, not as high as percents, probably, and the fluctuation may not be all that far when heating up 50C or something from high currents... so maybe it doesn't matter too much for your application, and maybe, if it does, you can just get a few resistors to put in parallel - lowering the current through each and reducing the temperature of each, reducing the change in resistance.
The 1% you mention is probably the initial tolerance, not the temperature coefficient.