Linearizing NTC thermistors is relatively easy; the same is not true for the typical polycrystalline PTC thermistor, which tend to have a more abrupt change in resistance vs. temperature (a nearly hyperbolic curve). Generally speaking, if you need to measure temperature then use an NTC thermistor.
560 ohms is a strange resistance value for a PTC thermistor. What was the original part number?
Hrm, not sure what kinds you're thinking of?
Ceramic NTC thermistors (the most common NTC type) have a grossly nonlinear curve, something like R = 1 / log(T) with constants (and higher order terms) thrown in. They can only be linearized in the Calculus sense: that, for a sufficiently small range of temperatures, the resistance changes proportionally (the curve locally approaches a tangent line). By placing (constant) resistors around the NTC, you can trade some gain for range, so that a wider range meets the same linearity spec (within so-and-so percent of linear), but that the absolute slope (|dR/dT|) is smaller as well (lower gain). (Here's a calculator that does the first part -- using Calculus to find the slope, and using resistors to tweak the slope -- but doesn't show range:
http://seventransistorlabs.com/Calc/Tempco.html )
There are two kinds of PTC resistors: metallic RTDs (doped Si, Ni, Pt and others), and resettable fuses based on conductor-plastic composites (the plastic melts and expands, and the metal particles separate, leaving a suddenly high resistance). The latter are nearly hyperbolic, and useless for temperature sensing applications (but handy for thermal and current protection, hence Polyfuses). The former are quite accurate, with lower noise than ceramic NTCs, and a wide linear range. The resistance is nearly proportional to absolute temperature, while minor tweaks can be done with resistors (linearize over a given range -- again, effectively Calculus at work), or by correction factors or lookup table (the approximating Taylor polynomials are usually given for these types).
I would think the OP has this type, but it's not clear why it would need to be linearized if it's replacing a PTC that's presumably already had that solved...
Tim