Quasi-collinear geometry is a special configuration of acousto-optic (AO) diffraction that provides an extremely large AO interaction length for achieving extremely high spectral resolution of AO tunable filters (AOTFs). Large AO interaction length also makes it possible to implement multifrequency diffraction in quasi-collinear AOTFs, which has found multiple applications in modern optoelectronics. The most widespread of them being ultrashort laser pulse shaping when the pulse shape and spectral composition is controlled by the spectral composition of the ultrasound pulse aroused in the AO crystal. The operation of quasi-collinear AOTFs is accompanied by the appearance of the temperature gradients in the AO device mainly due to the acoustic power absorption by the material. We experimentally assessed the influence of these gradients on the AOTF spectral characteristics. A theoretical model based on the Raman-Nath equations was proposed, which allows to consider the influence of ultrasound attenuation and temperature gradients on the AOTF transmission. This model is valid for transmission simulations both in single- and modulated-frequency AOTF operation modes. The study includes the effects of acoustic wave attenuation and AO phase matching shift caused by inhomogeneous crystal temperature along the optical beam path. The compensation strategy based on ultrasound frequency and magnitude adjustment is proposed for minimizing the effect of temperature gradients and acoustic field attenuation on AOTF spectral transmission for broadband operation in ultrashort laser pulse shaping.