Why did partner bid 3C??? Since I don't have an ideal call, my thought is to consider each of the possibilities and see what bid I can make that will do the most good, or at any rate do the least harm.
1. Partner wants ME to play the hand at three NT. Always a good choice with Trixie at the wheel. Even my good partners sometimes get a little tired and want a short break. If this is a live possibility, then I think that it is by far the most probable one. In that event 3NT is automatic.
2. Partner is slammish and wants to uncover a diamond fit when I give a diamond preference. Well, a simple preference does not show all that much support, my diamond holding could be worse, but I don't have real support, and my hand is only average minus in a slam auction. A slow 3D preference shows my hand but is outright cheating. I really don't like a 3D bid because, if pard takes it seriously, it might propel us into a 6D contract looking for the trump king and off another trick. If 6D is right, we might still get there after a 3NT bid.
3. Partner has three hearts and short spades and is looking for 4H or more or some number of NT. 3H is an outright lie about my suit length, but sometimes 4-3 major fits are the best spot. My spade holding argues that this is probably NOT one of these hands. So, 3H will likely work out OK, but I don't think it is the best bid.
4. Partner is 5-5 or 6-5 in the minors with enough cards to be slammish. In this case I don't got it for him/her. Only the AK of hearts is positive. So, in this case, 3NT is the best bid, and if pard bids 4C, I can give a forced, tepid 4D preference. Most often pard will pass 3NT, and we should be in the best spot. Play all misfits in NT (just kidding).
5. Partner has good 4 card heart support and 3C is the first step in a slam auction. In this case, I want to slow the auction down a little, and 3 NT will do that best. We should get to the right level in hearts with no problem.
The bottom line for me - 3NT!!!