I should point out that to some DMs, the dragon shaman's healing aura is a feature, not a bug, because it helps prevent PC deaths (yes, some DMs do find PC death troublesome to deal with and prefer to avoid it), and because it allows the PCs to continue adventuring instead of stopping and returning to a safe place every few hours or so because they are out of hit points and healing (yes, some DMs do find that this style of adventuring clashes with the way they prefer to run their games).
It is primarily a mechanism to reduce the risk of PC death and allow for quicker recovery of resources between fights. Its effects during the first few fights of the day are likely to be minimal since it only kicks in after at least one PC has been injured to less than half his hit points (naturally, this also depends on the PCs' luck and the relative challenge of the encounters).
If, as a DM, you prefer to run games where the risk of death is significant to the PCs, you could alter the aura so that it only restores hit points every minute (or longer) that a PC remains in its area of effect. This still allows it to perform its resource recovery function (although at a much slower rate), but prevents it from becoming useful as a means of stabilizing dying PCs in combat.
If, as a DM, you prefer to run games where the PCs have to manage their resources carefully, you could allow the aura to restore hit points up to one quarter normal hit points, or one tenth, or maybe to just stabilize a dying PC and bring him to one hit point.
Alternatively, you could just remove the aura from your games entirely. If you have Dragon Magic, it describes other auras that you could replace it with.
