The VLT-FLAMES Tarantula Survey has observed hundreds of O-type stars in the 30 Doradus region of the Large Magellanic Cloud (LMC). We study the properties of 105 apparently single O-type dwarfs. To determine stellar and wind parameters, we used the IACOB-GBAT package, an automatic procedure based on a large grid of atmospheric models calculated with the FASTWIND code. In addition to classical techniques, we applied the Bayesian BONNSAI tool to estimate evolutionary masses. We provide a new calibration of effective temperature vs. spectral type for O-type dwarfs in the LMC, based on our homogeneous analysis of the largest sample of such objects to date and including all spectral subtypes. Good agreement with previous results is found, although the sampling at the earliest subtypes could be improved. Rotation rates and helium abundances are studied in an evolutionary context. We find that most of the rapid rotators (vsini higher than 300km/s) in our sample have masses below 25 MSun and intermediate rotation-corrected gravities (logg_c_ between 3.9 and 4.1). Such rapid rotators are scarce at higher gravities (i.e. younger ages) and absent at lower gravities (larger ages). This is not expected from theoretical evolutionary models, and does not appear to be due to a selection bias in our sample. We compare the estimated evolutionary and spectroscopic masses, finding a trend that the former is higher for masses below 20M_{sun}_. This can be explained as a consequence of limiting our sample to the O-type stars, and we see no compelling evidence for a systematic mass discrepancy. For most of the stars in the sample we were unable to estimate the wind-strength parameter (hence mass-loss rates) reliably, particularly for objects with luminosity lower than logL/L_{sun}_ about 5.1. Ultraviolet spectroscopy is needed to undertake a detailed investigation of the wind properties of these dwarfs.