Does Resting Heart Rate Affect Calorie Burn?

Short answer: Yes

Slightly longer answer: The heart is a muscle. It pumps blood. The more times a muscle contracts, the more energy is required, and therefore the more calories are burned in the process.

Even longer answer: Obese people have, in general, higher resting heart rates. This is due to many factors, but one of the main factors is that being obese also means your heart and lungs do not work well together. In the vernacular, we call this "out of shape." The better "shape" you get into, the lower your resting heart rate becomes. This is of course, excluding the effects of any medications you may be taking or any medical conditions you might have. Not calling anyone obese here, just citing an example.
Speaking of medical conditions, hyperthyroidism (aka, Graves Disease) is an example of a medical condition where the thyroid is overactive and secretes too much thyroxine. Among other things, thyroxine increases your resting heart rate and basal metabolic rate (BMR). It should come as no surprise that many people with Graves disease have trouble gaining weight. They burn a ton of calories just maintaining their BMR.
There is a lot more that could be said, but I hope I answered your question.

As already stated, your resting heart rate will be higher if you are in worse shape. Mine was close to 90 at one point but it is now in the 60s as I do a lot of cardio.

Regarding the calorie figures, I would trust them from the polar as long as you have your metrics input correctly in the watch (weight, gender, age...). Even if the calorie estimate is a little off, it is probably much more accurate than the MFP figures.

I would not subtract calories based on having a higher resting heart rate.

Thanks. So I /should/ assume my calorie burn is lower than what the Polar tells me.

Is there any way to approximate how much to subtract from the Polar's reading?

Yes, it is likely lower. The inherent problem with all HRMs is that actual max heart rate varies fairly widely between individuals. The HRM estimates your max HR based on your age. If, as it sounds from your earlier comments, your actual heart rate is higher than the programmed number, then the HRM assumes you are working at near max effort--and that inflates the calorie number.

There is no fixed amount you can subtract from the total. If you get some idea of your max heart rate, you can program that into the FT7 and that would improve the accuracy of the calorie burn number.

Short answer: Yes

Slightly longer answer: The heart is a muscle. It pumps blood. The more times a muscle contracts, the more energy is required, and therefore the more calories are burned in the process.

While technically this is true. The mass of the cardiac "muscle" is small and so any "increase" in calorie burn due to an increased heart rate is negligible.

^^^ This

Short answer: Yes

Slightly longer answer: The heart is a muscle. It pumps blood. The more times a muscle contracts, the more energy is required, and therefore the more calories are burned in the process.

While technically this is true. The mass of the cardiac "muscle" is small and so any "increase" in calorie burn due to an increased heart rate is negligible.

^^^ This

The heart is the size of your fist and beats about 100,000 times per day, depending on your heart rate. I'd say "negligible" is a stretch. That's the whole idea behind HRM calorie trackers.

No, it isn't. The whole idea is that number of beats per minute + your body mass gets to a blood volume pumped per minute estimate; that plus an estimate of your fitness level / VO2max (i.e. how efficiently your body transports and uses oxygen in the blood) provides a proxy for how much oxygen your body is using to oxidize (i.e. burn) fuel, that is, calories.

It is NOT an estimate of the energy needed to pump the heart. That would be absurd.