Alrighty.
*Rolls up sleeves*
First of all, good job. Making a good counterpoint to the warlock is nice, and giving a good divine caster concept for charisma is great. I like the feel of it and I think the game needs more use of the traditional "dump" stats.
The big issue which has been well covered is the unlimited healing potential. I'm going to offer a different solution to the problem.
First. I'm not big on the side affects as a balance cocept, unless it fits the world concept. The player is going to have to plan ahead and make choices in combat anyway to run this character, just like any other spell caster, so no need to tone down the actual effect after he has decided to heal someone versus casting an invocation or attacking in combat or any other action he forgoes to use the ability. In other words, let the player have their powers and have fun. You want them to play your new class you worked on.
What I would do is limit the healing as a spell like ability (which means concentration checks to avoid AoO in combat) that can be cast a number of times per day equal to his wisdom modifier (or once/week with a negative modifier). You could use Charisma, I'm just throwing Wisdom out their do to 1) Thematic: Your reference to divine power being harder to control, and 2) I like the idea of special character classes having more stat requirements - that makes them special (like a paladin needing a number of good stats to run well). I just think specially classes should be a little harder and, well... special. Plus it puts the breaks on the healing a little more. That is just my 2 coppers.
Now the rest looks good. You followed the format of the Warlock which is good as far as rules goes; it uses existing rules making it easier for characters to know. It is tied to the Warlock which makes it an easy concept for players to “wrap themselves around”. And it follows a Wizards created class which means it was created by some of the best rule minds in the industry who should have play tested the class (although some prestige classes from Wizards has made me question this). I’ve noticed that Bruce Cordell’s name pops up on a lot of Wizard products dealing with magic, and if he did this class then it should be fine. The man does some great work (beware his dungeons – they are fabulous but also quite dangerous). I would play test it if possible, or come to an understanding with the first player to play it that “If it seems weak, I’ll boost it and if it is to strong, I may need to roll something back” kind of agreement. A good player will work with you.
The scratch and sniff test:
How does it compare to a base class, which it should not be better than. If you compare it to a cleric, which it is similar to because of the healing IMO (plus the healing is the balance issue), then you get the following:
Similar BAB, the Celestial Mage has reduced saves, lower hit points, and reduced combat proficiencies when compared to the cleric. On the plus you get a lot of special abilities. The cleric has limited special abilities (based on domain powers) plus every GMs bane, turn undead. The Celestial mage looks strong so far, but…
The mage has access to a limited number of invocations while the cleric has a vast spell selection but is limited by the number of times per day it can cast them. On the surface, it looks even.
High level comparison: A 15th level cleric with a 22 for Wisdom can cast 35 different spells per day (not including 0 level spells) plus 8 domain spells. A Celestial Mage with a 22 Charisma and 22 Wisdom can cast 9 different invocations, but can repeatedly cast those invocations all day. The Celestial Mage launches a Heal Blast 6 times per day for 7d6 healing – or an average 21 points of healing) as a ranged touch attack. The cleric can cast heal 4 times per day for 150 points of healing when he touches someone and still have 31 spells + 8 domain spells available.
Now unlimited invocations per day may sound pretty good to a cleric having 43 spells available, but there are some considerations. The invocations are not as powerful as the cleric spells and some invocation are used to affect the Celestial Mages main class feature – the Holy Blast. Also, it is doubtful that the cleric will find itself in a situation where he would actually burn through all of those spells in a day. It’s possible, but odds are it will be rare. Most groups go down when the spell casters get low on spells. That makes the number of spells/invocations available less important. When you combine that with the Celestial Mage having 9 different invocations and the cleric having a possible 43 different actual spells the scales tip heavily in favor of our friend the cleric.
In fact, I’d say the spell and healing capabilities out ways all of the special abilities of the Celestial Mage accept the holy blast. That is the factor that will either make the class equal to the cleric or a little weak. That probably needs to be seen in action to be judged, but looks pretty good.
In retrospect, my recommendation on the healing blast needs to be tweaked. At 3rd level, the Celestial Mage with a wisdom of 18 can heal someone for an average 6 points - 4 times per day while the cleric can cast a cure light wounds for an average 7 points – 4 times per day. Not bad. The 15th level casters from the example above show the gap in healing growing considerably. You may wish to consider either:
1) Allowing the Celestial Mage to add his level to the healing, like the cleric, or
2) Casting it more often then what I recommended to start. Perhaps the Celestial Mage starts out with 1 + Wisdom modifier at 3rd level then gets more castings as he raises in level, say an additional use every 3rd level.
Hope all of that helps out!