FWIW here is a snippet from Training and Racing with a Power Meter 3rd Edition (page 34):
“Relating the specified power levels to corresponding heart rate ranges or zones is somewhat difficult to do owing to the inherent variability of heart rate as well as individual differences in the power-heart rate relationship (even when referenced to threshold power). Nonetheless, approximate heart rate guidelines have been provided in Table 3.1 so that they ca be used along with power to help guide training, if desired.”
In other words, don’t get excited if the zones don’t line up.
Only during early base, or after taking time off the bike. During that 4-6 week period of time, upper zone1 and lower zone2 power will map to zone2 HR (Coggan zones). I normally cap efforts at the top of zone2 HR during this time. For me, top of Coggan z2-HR is 9bpm lower than Friel z2-HR.
Coming off early base, my aerobic decoupling will drop below 5% and I start seeing a lot of 0-3% decoupling. From that point forward, zone2 power will usually map to Coggan zone2/zone3 HR, and map to Friel zone2 HR.
Not much later in base I can do threshold efforts with almost no decoupling. Seems that both cardiovascular and metabolic fitness is good, and I see stable relationship between HR and power from aerobic endurance to threshold. Tempo and threshold workouts map to the same Coggan HR zones. Overall I find Friel HR zones to more accurately map to power zones, mainly because of z2 and z5/z6.
After a few months of base I can ride all day at Friel zone2 (130-143bpm) without major fatigue. Coggan’s guidelines for zone2 (111-134bpm) would have me riding much slower and no difference in fatigue the next day.
Given all that, I’m happy training to power zones most of the year. That means I usually ignore HR zones and use power zones to guide training. I do look at power-to-HR relationship of every ride, and what I wrote above is based on 4 years of reviewing power & HR data of every ride/workout. I’ve got a pile of century rides both flat and mountain, many in lower to mid tempo (by intensity factor), and all of those have an average HR in Friel zone2.
FWIW my inside HR is almost always lower than when outside, and I train in the garage without air conditioning (or heat) so the temperatures are comparable.