For a 10 minute effort ignore your heart-rate, if you try to get it up to a 'racing' rate in the first couple of minutes you'll be going out far too hard.
To get a feel of what it should be like (if you can measure distance/speed on your turbo) do 10 minutes flat out on the turbo, note the distance travelled and work out your average speed, have a 10 minute rest then ride again trying to get up to your original average speed within the first minute holding it there for the next 8 minutes and then go as hard as you can for the last minute. That should give you some idea of what an 'even-powered' ride is like.
When you race try to remember what the start felt like on the turbo and try not to overcook it off the start. When you get to halfway you can kill yourself as there's only 4 minutes left
If you're prepared to adjust your bike you can drop the handlebars as far as they will go (flipping stem over can help depending upon how it's set up already). If you're not comfortable on the tribars in that position moving the saddle as far forward as it will go may help. You want to aim to get the front as low as you can whilst being able to pedal in relative comfort. Importantly remember where everything was to start with as you'll curse me if you can't get back to your original position.
For a short ride you definitely need to warm-up. My warm-up takes just under an hour including faffing time:
5 minutes very easy
5 minutes easy
10 minutes working up easy-moderate pace
Get ready to race, helmet number etc, excess kit off
5 minutes moderate pace
5 minutes fast pace
Then:
3 x 45 seconds at race pace (not flat out, but what you will be racing at) with 3 minute rests in between.
15 minute spin to start
Doesn't matter whether you spin or push a big gear. I would guess they will gear-check you anyway so you won't have any choice. Make sure your gears comply.
Hills exactly as Paul says, important thing is to really push down the hill not take a rest as most people do.
Other things to remember:
Don't put a full water bottle on your bike for a 10 minute ride!
Check tyres for flints etc before you get on it and again when you're waiting at the start.
Make sure you know where the start, finish and any turns are.