The good news is that it is well known that varroa do not like high temperatures:
“Varroa mites prefer temperatures between 26 and 33 _C (Le Conte and Arnold, 1987, 1988; Patzold and Ritter, 1989; Rosenkranz, 1988), which are significantly lower than the normal temperature in the brood nest of approximately 34.5–35 _C (Becher and Moritz, 2009; Rosenkranz and Engels, 1994). Varroa mites are able to discriminate temperature differences of about 1 _C (Le Conte and Arnold, 1987).” (from P. Rosenkranz et al. ‘Biology and control of Varroa destructor’ Journal of Invertebrate Pathology 103 (2010) S96–S119)
See also US patent Beehive heater US 3994034 A and try Googling the website for VarroaController both of which seek to damage varroa by heating the hive typically above 40 Celsius.
The bad news is that such temperatures can also damage the sperm stored within the queen, typically sperm viability drops to 20 percent from about 90 percent. See: Pettis JS, Rice N, Joselow K, vanEngelsdorp D, Chaimanee V (2016) ‘Colony Failure Linked to Low Sperm Viability in Honey Bee (Apis mellifera) Queens and an Exploration of Potential Causative Factors’ PlosOne 12 May 2016: