Nope. I've seen 400W halides with SPS and clams over a 20H before. I have no idea what effect this had on temp, but the inverts seemed very happy.
For what it's worth, you'll get better mileage out of a 20-long for $30. The extra few inches will still get enough light to grow lower-light sps like montis and birds nest (not to mention plenty of zoas, paly, or mushrooms).
More square footage for that light to spread out on. I have a 20L with a 4X24 T5.
That, the the tank is a bit shallower which makes it easier to work around in.