Fuel ignition potential is one of the primary drivers influencing the extent of damage in wildland and wildland-urban interface fires and it is a decisive factor in planning prescribed fires. Determining the susceptibility of fuels, which vary spatially and temporally, to fire will help to recognize necessary defensive actions, reduce damages, and help to configure prescribed fire plans. In this paper, the development of a new computational model, Complex-environment Temperature and Moisture Predictor (CeTMP), is presented. CeTMP predicts the diurnal temperature and moisture content variations, and thus vulnerability to ignition, of objects/fuels with complex shapes, settings, or topography and materials under variable environmental conditions. The model is applicable to complex scenarios (e.g., interface or intermix communities) composed of natural and manmade random-shaped items in open atmosphere under the influence of local weather and diurnal solar radiation. The vulnerability of fuels to ignition is determined by predicting the transient temperature and dryness of fuel in connection with the surroundings, topography, and local environment, as well as flame heat if any exists. In this regard, a detailed surface energy balance analysis, coupled with a water budget analysis, is performed in high spatiotemporal resolution. The model performance was validated against several existing analytical and measured data. The discrete, high-resolution surface temperature and moisture content information obtained from the model can also provide unsteady boundary conditions for computational fluid dynamics simulations when coupled physics is desired.