Meh, not my experience. I found the lighter tuners to be less temp sensitive as opposed to the heavier tuners were typically good for about a 20-30 degree temperature swing, +/-15 degrees each way before I had to start changing settings to keep in tune. The one I use on my 18" anschutz 1712 medium barrel weighs only around 3.5 oz IIRC. They made me take it off as it is considered an "attachment" and therefore illegal for hunter class in silo. I did not see shifts in temp like the heavier tuners. I could use that one year round without adjusting it.
Lets keep in mind we are influencing barrel harmonics with weight, it is that simple. What is hard is knowing where and how much weight to place. I've seen an ARA benchrest barrel that that simply did not group well at around 3/8-1/2" even with a harrels tuner, but absolutely came alive and grouped very well when a mid barrel tuner was installed in addition to the harrels. That person then used that barrel for at least the next 4 years in competition. General rule of lighter and longer barrel responds better to tuner, but short and fat will still see changes. Any weight on the barrel makes a change of some sort.