As others mentioned, you don't have to calculate the Steinhart-Hart equation to display the temperature. A lookup table with interpolation between points is one way. Another is to use a polynomial interpolation (something akin to: T = a + b(R) + c(R)^2 + d(R)^3 + ...). The Pixaxe can manage multiplication.
Tracy Allen of EME Systems has several pages describing interpolation and table lookups for approximating 'difficult' curves on the BasicStamps. One page is
here. A specific application with thermistors is down the page (
here). Tracy also describes logarithm calculations in the same page. His examples can be translated to the Picaxe.
(I must be old: We had to memorize log tables in school).