<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((\mathcal {X}, d, \mu )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="script">X</mi> <mo>,</mo> <mi>d</mi> <mo>,</mo> <mi>μ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> be a metric measure space satisfying the volume doubling condition. In this paper, the authors provide a new and direct method of constructing stochastically complete (signed) heat kernels by virtue of the multiresolution analysis (for short, MRA) structure. For any <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\beta \in (0,\infty ),\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>β</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mi>∞</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> two kinds of applications are given: (i) via taking a non-smooth MRA generated by Haar wavelets, such construction gives rise to a heat kernel satisfying only stable-like upper estimate of index <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\beta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation> (no continuity and near-diagonal lower estimate); (ii) via taking a smooth MRA generated by smooth wavelets/splines, such construction gives rise to a signed heat kernel (no positivity) satisfying the stable-like upper estimate of index <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\beta ,\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>β</mi> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> as well as the almost Lipschitz regularity and the near-diagonal lower estimate.</p>