## 1 Introduction  
Solving a heat conduction problem is to determine temperature histories within the heat-conducting material [1; 2; 3]. Because the boundary conditions are often difficult to directly measure in industrial practices, the requirements for recovering the missing temperature render the problems into an inverse heat conduction problem [4]. The heat conduction problems are categorized into initial value problems, which have been extensively solved by meshless methods such as the method of fundamental solutions (MFS) [5], the radial basis function collocation method (RBFCM) [6; 7; 8],the element-free [PERSON] method [9], the radial basis function finite difference method [10; 11], and the local radial basis function-based differential quadrature method [12]. For time discretization in most published works, the time-marching methods such as the implicit, explicit, Crank-Nicolson or Runge-Kutta schemes are often adopted by approximating at each time interval [13; 14; 15].  
Even though the success of numerical methods combined with the time-marching scheme is effective and easily implemented for dealing with heat conduction problems, limitations remain while utilizing the time-marching scheme including a small time interval for the convergence [16; 17]. As a result, the time-marching methods for solving heat conduction problems may be computationally expensive. Recently, several numerical approaches based on the space-time scheme have been proposed [16; 17; 18; 19; 20]. [PERSON] et al. proposed the space-time finite element method (FEM) for the computation of fluid-structure interaction problems [17]. The space-time discontinuous Galerkin FEM has been proposed and applied for dealing with compressible Navier-Stokes equations as well as advection-diffusion problems [21; 22]. Meanwhile, a collocation approach regarding space-time exponential basis functions for wave propagation problems, static and time harmonic elastic problems have been developed [23; 24; 25]. A new boundary-type meshfree technique incorporated with the space-time collocation scheme for modeling of heat conduction problems, as well as tide-induced groundwater response, have been also developed [20; 26].  
The space-time collocation approach using the radial basis function (RBF) can be traced back to [PERSON] and [PERSON] [27]. Moreover, [PERSON] et al. developed the RBECM using the space-time scheme for solving parabolic and hyperbolic equations [28]. Despite the success of the RBFs with the shape parameter as an effective numerical scheme for solving partial differential equations, the selection of the shape parameter may still dominate the accuracy of the results [29; 30; 31].  
In this study, the pioneering work using the collocation scheme based on the space-time radial polynomial basis function (SRPBF) for modeling the transient heat conduction phenomena is first proposed. The randomly unstructured points are collocated in the space-time domain, where both boundary as well as initial data may be regarded as space-time boundary conditions. The SRPBF is constructed by incorporating time-dependent exponential function into the radial polynomial basis function. Since the SRPBF is nonsingular and infinitely smooth in nature, the shape parameter is not required in the proposed approach. Result comparison between the proposed method and that from the RBECM with the time-marching scheme is conducted. The article is organized as follows. In Section 2, the SRPBF is introduced. In Section 3, we present the validation, accuracy, and convergence of the proposed approach. The comparison of results with the RBECM with the time-marching scheme is then illustrated. Three examples of heat conduction are given to demonstrate the stability of our approach in Section 4. Findings are concluded in Section 5.