Your heap as it stands is anaerobic - which means it doesn't get hot and weed seeds remain viable. You can improve the speed with which it degrades and the heat it produces by turning it regularly, making sure its damp enough and covering with something (an old piece of carpet) to keep the heat in.
Unless you buy a compost bin which has a means of turning or stirring or shaking up the compost, it won't get much hotter than your current heap.

As Bamboo says, if you put a lot of effort into your compost you will get a better product. Most gardeners, including myself, don't do this. A modern plastic compost bin will have the same results as a traditional bin. I now use plastic bins because my old, wooden, New Zealand bins rotted away. The compost coming out is just the same, weed seeds included.

I think your way is just as good, but you need to cover it with some old tarpoling and every so often turn it. Traditional methods are tried and tested for centenaries and modern life quick fixes are OK but don't always cut the mustard. Ask any woman that has tried the quick fix diet it never works or lasts. haha.
Seriously it doesn't affect the results so stick with what you know.

I have a compost bin and it now seems to be working reasonably well. It was slow to start but in the second season it was beginning to rot down. The problem with my bin is getting to the compost! There is an inspection panel at the bottom of the bin but if you want to remove compost from there, the fresh stuff falls inot the space! The bin really need to be lifted to access the compost and I have yet to try this. Maybe next year...........

I have a bin like yours in my neighbours garden, Somhairle. I have found the best way to get at the compost is to treat the bin as a childs bucket on the beach - lift the cover off and there is a nice heap of compost. I relocate the cover to one side and put the fresh waste from the top of the heap back into the bin. Quite easy.

Thanks for all your comments.

It seems from your comments that my composting method is OK so I'll stick with my heap.
We have tried a bit of old carpet over the top of the heap in the past and that did seem to improve things. So I will keep it covered in the future with another piece.

I will attempt to turn over the compost once in a while. I hope the worms won't take too badly to this!

Thanks again.

Bulb, do you turn yours? I havent as I find it a bit awkward with the plastic bins, wonder if it makes a big difference. I dont have grass cuttings in there, just kithen waste and weedings.

Hi, Dawnsaunt. No, I have never bothered to turn compost in a bin - lifes too short. My compost does have weed seeds in it so I have learned to bury it in the veggie garden. I did, just once, use it as a mulch - never again - instant greenery :-(

Thanks Bulb, that's a relief as I've not turned mine and the stuff in 2 of my bins looks nearly ready. I'll put it on the veg plot then, when do you suggest, Winter and to dig it under?

Just whenever, Da, I tend to mark out the rows where the veggies will be sown, dig a trench and put the compost in the bottom, then fill the trenches in and mark them. This can be done anytime over the winter and the trenches will be ready for sowing in 2012.

Thank you very much Bulb :-)

Thanks for the advice Bulb. I'm not sure I have the space to move it to one side - it is strategically positioned to be non-intrusive!

And, I do mix mine with a fork. It is a pest, but I have always thought it best to get a mix of materials.

Today I emptied 2 of my black plastic compost bins. Lifted them up as Bulb suggested to reveal the heap. So pleased with it, got the bins in June 2010 and I have lovely compost - got 3 heaped barrow loads from each one, just like well rotted manure without the smell. In a pile now on the veg plot. Never turned mine once, I do avoid putting weeds in seed in there and no grass cuttings as our mower mulches.