We present infrared spectra for a heterogeneous sample of 22 starburst galaxies. Line fluxes are measured for the prominent He I 2.058-mu m and Br gamma lines, and their ratio is compared with theoretical predictions of the behaviour of the He I 2.058 mu m/Br gamma line ratio with stellar effective temperature. The observed line ratios are lower than those found in individual compact HII regions. For a subset of these galaxies optical measurements of HeI/H beta were derived from the literature. The combination of optical and infrared HeI/HI line ratios suggests effective temperatures for the UV field of at least 40 000 K, consistent with existing results from metal-line excitation.