## Materials and Methods
### Characterization  
The particle sizes of kaolin, feldspar, and quartz were measured using a Malvern Mastersizer 2000. The loss on ignition, LOI (%), of the fired samples was calculated via the following equation, [26]  
\[\text{LOI}\%=\frac{W_{D}-W_{I}}{W_{D}}\times 100 \tag{1}\]  
where \(\text{W}_{D}\) is the weight of the green body and \(\text{W}_{I}\) is the weight of the ceramic after the firing process. The sample linear shrinkage in length (Ls) was calculated as Equation (2) [24]  
\[\text{Ls}=\frac{L_{0}-L}{L_{0}}\times 100 \tag{2}\]  
where \(\text{L}_{0}\) is the length of the green body and L is the length of the ceramic after the firing process.  
The bulk density, water absorption, open porosity, and bending strength properties were measured according to EN ISO 10545. [27] Briefly, the dry mass (D) of the sample was measured first. Then, the sample was immersed into boiling deionized water for 5 h and soaked for 24 h at ambient temperature, then mass (S) of the sample suspended by fine wire in water, and the water-saturated mass (W) was weighed. The total volume (V) of the sample can be measured by \(\text{V}=\text{W}-\text{S}\).  
Bulk density (B) can be calculated via Equation (3).  
\[\text{B}=\frac{D}{\text{V}} \tag{3}\]  
Water absorption (WA) (%) is calculated via Equation (4).  
\[\text{WA}\%=\frac{W-D}{\text{D}}\times 100 \tag{4}\]  
The open porosity, \(\varepsilon\) (%) can be described as Equation (5).  
\[\varepsilon\%=\frac{W-D}{\text{V}}\times 100 \tag{5}\]  
Figure 1: Scheme of the fabrication process of the ceramic composite with carbon fiber.  
The specimens were then cut into a size of 30 \(\times\) 20 mm with the thickness of 4.5 mm by a Struers Accuton-100 cut-off machine for mechanical and electrothermal performance tests. A three point flexural test was used to measure the mechanical properties of the obtained composite samples. This flexural strength test was carried out using an Instron 5567 universal testing machine with a span of 20 mm and a cross head speed of 0.5 mm/min. L represents the support span (mm); b represents the width of test samples (mm); d is the thickness of the tested sample (mm); and F is the load at a given point on the load deflection curve (N). The bending strength \(\sigma_{\mathrm{f}}\) is calculated via Equation (6). [27]  
\[\sigma_{\mathrm{f}}=\frac{3 FL}{2 bd^{2}} \tag{6}\]  
The samples were fractured in liquid nitrogen and the scanning electron microscopy (SEM) images of the fracture surface was then obtained by scanning electron microscope (LEO SEM S440 from Carl Zeiss, Germany). The powder x-ray diffraction (XRD) patterns of the samples were collected by an x-ray diffractometer (Analytical/X'Pert Powder) using Cu K\(\alpha\) radiation (\(\lambda\)\(\sim\)1.54 A) over a range of 5 to 70\({}^{\circ}\) (20) at a rate of 2.4 \({}^{\circ}\)/min. The carbonization degree of carbon fiber was characterized by Raman spectrometer (Renishaw inVia Raman Microscope) at a laser wavelength of 514 nm. The spectra were collected at 10% of the nominal power (50 mW) for 10 s. The carbon fibers were extracted from the composites and washed for 30 min by sonication before characterization. The obtained carbon fibers were denoted as CF-1200, CF-1250, CF-1300, and CF-1350. For comparison, the pre-oxidized PAN fibers were put into the furnace without ceramic precursor and fired at 1200 \({}^{\circ}\)C, which was named as PAN-1200.  
The electrical resistance of the as-prepared samples were measured by a multimeter (FLUKE 189). Infrared thermal imaging technology was used to characterize the electro-thermal performance. The composites were connected to a power supply (KORAD, KD3005D) at 2 V to 5 V and the joule heating performance was recorded by a thermal camera (FLIR ONE PRO).