  Refractive optics in astronomical instruments are potentially sensitive to
temperature gradients and temperature transients. This sensitivity arises from
thermally dependent refractive indices, lens spacings, and lens dimensions. We
have therefore undertaken a detailed thermal analysis of Binospec, a wide-field
optical spectrograph under development for the converted MMT. Our goals are to
predict the temperature gradients that will be present in the Binospec optics
and structure under realistic operating conditions and to determine how design
choices affect these gradients. We begin our analysis by deriving thermal time
constants for instrument subassemblies. We then generate a low-resolution
finite difference model of the entire instrument and high-resolution models of
sensitive subassemblies. This approach to thermal analysis is applicable to a
variety of other instruments. We use measurements of the ambient temperature in
the converted MMT's dome to model Binospec's thermal environment. During
moderate conditions we find that the Binospec lens groups develop 0.14 C axial
and radial temperature gradients and that lens groups of different mass develop
0.5 C temperature differences; these numbers are doubled for the extreme
conditions. Internal heat sources do not significantly affect these results;
heat flow from the environment dominates. The instrument must be periodically
opened to insert new aperture masks, but we find that the resulting temperature
gradients and thermal stresses in the optics are small. Image shifts at the
detector caused by thermal deflections of the Binospec optical bench structure
are approx 0.1 pixel/hr. We conclude that the proposed Binospec design has
acceptable thermal properties, and briefly discuss design changes to further
reduce temperature gradients.
