I own a number of properties in Canberra and in the region, and have noticed that some suburbs are priced very strangely compared to similar properties in similar suburbs. For example, over the past few years I have bought 3 properties in Braddon, and the most I paid was $322k which was a nice 2 BR unit with secure parking. Have a look at what is available in Braddon, now, and what it costs.
http://www.allhomes.com.au/ah/act/sale-residential/braddon/121483810
Ignore the first half of the page - these are all semi-commercial serviced apartments.
The trick with the Canberra market is not to fight it. There are lots of people in Canberra who get really attached to specific suburbs, and especially to general areas (ask a Canberran about the north versus south thing...). Many of these people will continue to rent rather than buy in a different suburb or area.
Now, I must say that the $700 a week for the 2 bedroom apartment "close to work and school" must be in one of the most expensive suburbs in town, because even for Canberra, that's a lot. Instead of doing this, try instead looking along the major bus routes for something further out. Or look just over the border in NSW. There are beautiful properties (free standing homes) available in Queanbeyan (15 mins drive from the centre of Canberra, 25 mins in peak hour) from $500k.
Back to whether the Canberra market is heating up... There are lots of people whinging in Canberra about the ridiculously, outrageously, impossibly high house prices. And frankly, I think the market will get higher before it corrects, especially in certain suburbs which are underpriced given their location. Bear in mind too that there are LOTS of people in Canberra who seem to think it's their God-given right to eat out several nights a week at pricey restuarants, drink expensive beers (there's a pub near my work that serves $28 pints), and travel overseas whenever they feel like it. The thing that is a bit scary is supply, or more specifically, the lack of it. Over the past 12 months I've watched supply dwindle. There's no much land being released by the government, and they want a lot of $$ for it. There is also the problem is expensive builders and tradies, meaning new property costs are high.
Me, I'm not that concerned, because my properties were all bought significantly below current market, and my rents are trending upward nicely. Not that this is very helpful for anyone else...