Compost tumblers work way better on well ground high-nitrogen material. If you grind everything you put in really well, it will get hot. I've had many folks ask me why their compost wasn't getting hot, and when I looked at it, it was in large pieces, either that or mostly carbonaceous material. I think your's is probably the first. I encourage these folks to invest in a compost shredder. This little electric machine will grind up food waste, leaves, clippings, etc, into small pieces. Putting it through twice is even better.
Here's the fastest composting process I've used:
Fill the compost tumbler to 2/3's full, with 3 parts well ground food scraps, well ground very green grass clippings, etc, and 2 parts of well ground leaves, cornstalks, etc. Adding manure or a compost activator really helps. Adding more scraps a bit at a time is more suitable for a layering method than to a tumbler, especially if not ground.
Turn twice a day, at least. You cannot turn it too often. Make sure you do a good job each time, or anaerobic decomposition will start messing with the process. The mix will heat up rapidly, unless the temperature is far below freezing.
Measure the temperature every other day. In a week or so, sometimes two, the temperature will drop. The compost is ready to move out of the tumbler. stack it in a tall pile on the ground, or in a wire bin.
Let it mature, and become very soft and humusy. I often leave it for a month, then stir it up, stack it, and leave it for another couple weeks, when it is particulate in texture, black, soft, and test high in nutrients.
Adjust the pH if necessary, and apply.
Now, there are much simpler and easier methods, but not as fast. You also don't necessarily have to wait for it to completely mature, and can use it as soon as it cools down, but the compost still has shrinking to do, and the pH will not really be stable yet.
Usually, I use a layered open pile, because I don't usually have enough material at one time to fill the tumbler with a batch.