Hi there!
Another simple device is the LM3914/LM3915 (same device all things considered). It's called a Dot Bar Display Driver (used for LED bar graphs). There are loads, have a look for one that suits your goals if the idea appeals to you.
I used this with the LM35 to make a bar graph LED thermometer, it's relatively simple to set the "temperature range" using a couple of resistors.
You could scale the voltage reference/temperature range of the 3914 (or 3915) to use, for example, the first or second, middle and last outputs for your three LEDs, and I would imagine could leave the other outputs floating; you can even get away with using no current limiting resistors on the LEDS, but not recommendable.
Using this device you can really simply set all three to be on at 60ºC or one by one, bar graph or dot mode. It is very easy and low parts to use, but like all these things the devil is in the detail of calibrating it right, which can take a bit of fiddling, a trimpot or two (or a potentiometer/variable resistor) would make this easier than using 2 fixed resistors to set the scale/temperature range.
Being adventurous, if you want grossly minimal (I don't recommend it!), and if you have a liking for maths and experimentation you could calculate resistor values based on the voltage drop of each LED you have ( they're not all the same in this respect), the LM35 output, and the power supply voltage, and the current you want each LED to draw; if 5mm green or red LEDS from a dim 5mA to a worryingly bright 20mA; blue LEDs are higher current, some are maybe 30mA, and in practice I found some blue or white LEDs need a larger value resistor to avoid being dazzling - but in the end it has a lot to do with the current limiting resistor you opt for each LED.
The disadvantage, if it is one, to this approach is that at 60ºC all three would be on; and another is that it might be hit-and-miss re temperature signalling at those specific temperatures.