Assuming, as mentioned in the question, that the user is protected from the effects of the sword, heat would not be an issue. As long as the user is holding the sword, he is protected from its heat. However, there are other issues.
Time and Convenience
If the sword heats up for only 1 minute, after 15 mins of recharging, then that's hardly efficient. That's a 15:1 ratio. Thus, seeing as a battle could last for several hours, the sword would then need at least a couple of days prior to the battle to charge. This would, of course, be an issue and a nuisance, because you may never know when the sword and its intense heat function may be needed, or for how long. With such an inefficient power output ratio, it may well be that the sword's intense heat function might rarely be used, if ever, simply because it just takes way too long to charge.
How would the user know how much power is left in the sword, before it needs to be re-charged? It is possible that the user may come across a situation where the intense heat function is desperately needed, but activates it, only to find that there isn't enough power to heat the sword up for longer than a second. Some sort of timer should be incorporated into the sword to inform the user how much longer the sword can produce such heat.
The user may be protected from the heating effects of the sword, but not everything around him or it. The obvious housing for such a sword would be a scabbard, but then the scabbard would also have to be protected from the heat. This is so that the scabbard does not instantly explode in a cloud of ash if the sword is accidentally activated inside the scabbard. Especially because scabbards are usually made of wood, or leather. The scabbard could be made of the same material as the sword, of course, since the sword is not damaged by the heat, but that would make the scabbard very heavy. If, on the other hand, the material used to make the sword is light enough that the scabbard would not be a hindrance, then the sword itself would not have enough force when used, because it is too light.