Flying endothermic insects thermoregulate, likely to improve flight performance. Males of the Sonoran Desert bee, Centris caesalpiniae Cockerell, seek females at aggregations beginning at sunrise and cease flight near midday when air temperature peaks. To identify the thermoregulatory mechanisms for C. caesalpiniae males, we measured tagma temperatures, wingbeat frequency, water loss rates, metabolic rates, and tagma masses of flying bees across shaded air temperatures of 19 to 38°C. Surface area, wet mass, and dry mass declined with air temperature, suggesting that individual bees do not persist for the entire morning. The largest bees may be associated with cool, early mornings because they are best able to warm themselves and/or because they run the risk of overheating in the hot afternoons. Thorax temperatures were high (38 to 45°C) and were moderately well-regulated, while head and abdomen temperatures were cooler and less controlled. Abdomen temperatures converged on thorax temperatures as air temperature rose, indicating active heat transfer from the pubescent thorax to the relatively bare abdomen with warming. The mass-specific metabolic rate increased with time, air, and thorax temperatures, but wingbeat frequency did not vary. Mass-specific water loss rate increased with air temperature. Using a heat budget model, we showed that whole-body convective conductance increased through the morning, and that the primary mechanism of regulating thorax temperature during flight for these bees is increased use of the abdomen as a convector at higher air temperatures. 

Carbon dioxide and water vapor emission measurements: To determine the metabolic and water loss rates of C. caesalpiniae large morph males during flight, we used flow-through respirometry. We stationed the setup underneath an outdoor, shaded porch less than 100 m from the locations where bees were captured to measure bees in conditions as close as possible to that of their natural, ambient conditions. Shaded air temperatures ranged from 19 to 38°C across and within four days of measurements.

We calculated average CO₂ and H₂O levels for 2-3 minute periods when bees were observed to be steadily hovering. We recorded flight behaviors for each bee, but all bees flew well and consistently, and we found no relationship between our flight behavior scores and flight metabolic rates, so these behavioral data are not reported.

To measure shaded air temperature, we used a BAT-12 thermometer and thermocouple. To assess that the metabolic chamber was perfectly air-tight, we measured CO₂ and H₂O levels over three to four minutes without an animal in the chamber; under these conditions, there were no significant changes in CO₂ concentration. The 95% washout of CO₂ from the metabolic chamber occurred in approximately 90 seconds.

Bee tagma temperatures: Immediately following the respirometry measures, we transferred the bee into a plastic bag, which we flattened onto a Styrofoam board to reduce conduction and restrict the bee’s movement. We then measured the head, thorax, and abdomen temperatures (T_h, T_th, T_ab, respectively) in random order within five seconds after cessation of flight by inserting a hypodermic thermocouple (Physitemp, MT-29/5HT Needle Microprobe, time constant = 0.025·s) into the center of each tagma. We recorded the tagma temperature data with a Pico Technology USB TC-08 Thermocouple Data Logger (Tyler, TX, USA). We recorded the shaded air temperature values following the temperature measurements for each individual. We calculated the temperature excess ratio (R_tagma) using Equation 1 (Baird, 1986).

Wingbeat frequency and flight score: We recorded the sound of wing movements during hovering flight in the flight chamber prior to each respirometry measurement for 20 to 30 seconds using the iPhone 7+ microphone. After the wingbeat frequency measurement, we closed the chamber to flush CO₂ and H₂O before the respirometry measurement. Using a sound editing program, Audacity version 2.4.2 for Windows, we visualized the wingbeats. We calculated average wingbeat frequency by dividing the number of wing beats by the time duration for three separate measures of 10 wingbeats.

Total body surface area calculations: We used a digital caliper (accurate to 0.01 mm) to approximate body surface area using geometrical calculations. We assumed that the head of the bee is a cylinder, measuring head width as the diameter and head thickness as the height. We assumed that the thorax is a sphere measuring thorax width as the diameter. We assumed that the abdomen is a cylinder and a cone, with the 1st through 3rd terga of the abdomen being the cylinder and the 4th and 5th tergi being a cone (Roberts and Harrison, 1999).

Heat budget model calculations: We assumed that bees were flying at thermal equilibrium between 19°C and 38°C in steady-state conditions. This assumption is supported by observations for honey bees that body temperatures are stable during 1-5 min of flight (Roberts and Harrison 1999), the prolonged steady hovering exhibited by most of our bees, and the steady CO₂ emission traces we observed. Q_metabolic and Q_evaporation were calculated from VCO₂ and VH₂O. Bees have mostly been reported to utilize carbohydrates as fuel for flight (Bertsch, 1984; Gäde and Auerswald, 1999; Suarez et al., 2005). Therefore, we assumed a respiratory quotient of 1 and 21.4 J*mL^-1 CO₂ to calculate metabolic heat production in Watts. We then multiplied by 0.96 (the fraction of power input liberated as heat during flight) (Ellington, 1984; Harrison et al., 1996; Roberts and Harrison, 1999). To calculate evaporative heat loss in Watts, we multiplied VH₂O by the latent heat of evaporation of water, 2.45 J*mg^-1 H₂O.

As we performed respirometry measurements in shade, we assumed shortwave radiation to be negligible. We summed the longwave (infrared) net radiation (R_loss – R_gain) for the head, thorax, and abdomen of each bee using the Stefan-Boltzmann equation.

We assumed that the bee’s emissivity, ε_s, is 0.97, and that bee surface temperature equals bee internal temperature (Stupski and Schilder, 2021). We assumed that the bee’s body surface absorptivity, a, is 0.97, that the emissivity, ε_c, of the glass metabolic chamber is 0.90, and that air temperature equals the wall temperature, T_i, of the glass chamber (Campbell, 1977; Ray E. Bolz and Tuve, 1973; Stupski and Schilder, 2021). To estimate whole-bee radiative exchange, we summed Q_radiation for the head, thorax, and abdomen and multiplied by tagma surface area.