How to Label a Heuristic Proof

Question

I am using \newtheorem{thm}{Theorem}[section] and would like to my article to read Heuristic Proof instead of the standard Proof. I am showing Ito's but not in a rigorous way. Any ideas?

\begin{Heuristic proof}
Since $g(x, t)$ is twice continuously-differentiable, we can apply Taylor's expansion to get 
\begin{align*}
dg(W,t) &= g(t+\Updelta t\,,\,W+\Updelta W) - g(t\,,\,W)\\
&= \frac{\partial g}{\partial t}dt + \frac{\partial g}{\partial x}dW + \frac{1}{2}\frac{\partial^2 g}{\partial x^2}(dW)^2 + \frac{1}{2}\frac{\partial^2 g}{\partial t^2}(dt)^2+ \frac{1}{2}\frac{\partial^2 g}{\partial t \partial x}(dt)(dW) + \dots\,\,(*)
\end{align*}
\end{Heuristic proof}

Answer 1

The following defines a new proof-like environment in which the proof title is temporarily changed to "Heuristic Proof" (despite my own reservations of the use of the word heuristic in these circumstances!), implementing lockstep's idea from the comments but in such a way that the original proof environment still exists.

\documentclass{article}
%\url{http://tex.stackexchange.com/q/110653/86}
\usepackage{amsthm}

\newtheorem{thm}{Theorem}[section]

\newenvironment{hproof}{%
  \renewcommand{\proofname}{Heuristic Proof}\proof}{\endproof}

\begin{document}

\section{Demonstration of Proof Techniques}

\begin{thm}
Almost all primes are odd.
\end{thm}

\begin{proof}
There are an infinite number of primes, only one of which is even.
\end{proof}

\begin{thm}
Almost no primes are even.
\end{thm}

\begin{hproof}
Well, it's just obvious, innit?
\end{hproof}

\begin{thm}
Almost every prime is red.
\end{thm}

\begin{proof}
You can tell I'm running out of ideas here.
\end{proof}

\end{document}