Is it OK to run above my MAF HR during hot days?
If you intend to do MAF (aerobic) training, the answer is absolutely not. The reason your heart rate spikes when it’s hot is due to weather stress.
The body's thermoregulatory response (which includes sweating) uses up a lot of energy. The skin is the largest organ in the body, meaning that it may well be the most costly system to run besides the brain). Now consider that the MAF HR corresponds to the intensity at which you're burning the most fats. If you start sweating, your body will need more energy. If it is not able to get that from fats, it'll get that from sugars. That heart rate spike is a direct indicator that your aerobic system isn’t powerful enough to drive the cooling system, meaning that your body is using anaerobic energy channels to be able to sweat at the rate it needs to.
Here's a second piece of the puzzle: the hormone responsible for activating the systems that increase the availability of sugar is cortisol, which is the primary stress hormone. This means that as soon as the demand for fuel exceeds the supply of fats, the stress on your body will increase by virtue of it increasing the availability of sugar. As the thermoregulatory system uses up sugar, cortisol will have to increase yet again, in order to expand the availability of sugar in the face of a dwindling supply.
(And I've mentioned nothing of the autonomic fatigue (of the nervous system) due to a higher heart rate, which only compounds the stresses I described above).
This means that increasing your target heart rate commensurate to increases in ambient temperature will very quickly turn a theoretically aerobic workout into an extremely stressful endeavor. Because the aerobic system---not to mention the body's ability to recover and grow---depends on a <em>lack</em> of stress, there's very little chance that the aerobic system can grow from such a workout.
(The thermoregulatory response may develop in spades, but part of the problem is believing that we're developing one system while actually developing another).
Since aerobic function is based on heart rate, so is exercise intensity. So, even if you’re going slower because it’s hotter, as long as your heart rate is the same, you’re still training the body as a whole at the same intensity. Although you’re not training your muscles as much, a powerful sweating system contributes a lot to your athletic output. By training it, you are expanding your athletic potential as surely as by running faster.