I too am in perth and know all about avoiding exercise claiming it's the heat! good on you for getting out and about =)
The best thing I've done is join the pool- yes, thirty passes is $116. So what I did to justify spending that amount is I went through my bank accounts with a highlighter and added up every take out (including cafe's etc) and figured that if I can afford to spend those $$ a month on crap, I'd transfer it to spending it on my health. I love going to the pool because - No one can see you sweating or panting, it's a total body work out and there is absoloutely no judgement from other people on what you're wearing or how fast you're going- hell, you can be wearing snorkle and goggles, using a kickboard and swimming flippers and no one looks twice at you in the swimming lane.It's also good think space, but if you find it boring you can buy underwater mp3 casings from H20 audio for around $100 that clip onto the back of your goggles =) .
I also have a jetts gym membership, it costs me 20 bucks a fortnight and the atmosphere is quite friendly. I was quite aprehensive about going to the gym too as I have the same concern as you- ARRRGH! PEOPLE ARE LOOKING AT ME AND THEY CAN SEE MY FAT MOVING AND HOW MUCH IM SWEATING!- but then my best friend said something that has stuck with me. PEOPLE ARE NOT LOOKING AT YOU AS OFTEN AS YOU THINK. They are too concerned about their own jiggly bits/red faces/cramp in their left leg and honestly don't care about how many km's you have run, what you're wearing or how many reps you've completed on the weights.
Hope that helps, getting over the mental barriers is half the battle, i find people are just impressed you're there, exercising and making an effort to care about your health- not thinking that your bathers are mismatched or you only swam 250m or you're only using the 3kg weights.