Your beer will be fine, and probably even benefit from sitting a little longer so I wouldn't worry. No need to rush it if you have the rest of your kegging equipment and you're just waiting for one thing.
In fact, a lot of people do one of two other things you could think about. Some naturally carb up their keg. Just like you'd carb bottles by adding corn sugar, you can carb up your keg like one big bottle by adding corn sugar. Search the forums for that and you'll get a lot of posts talking about it. The other thing people do is fill their kegs and then let the kegs sit for another few weeks at room temp to further condition just like you'd do with bottles.
So, technically, you could keg your beer right now and use sugar and get it started by carbing naturally, or just keg it and let it sit and continue to age in the keg for a bit until you get your temp controller and are ready to begin serving.