An ability to insert electronic/optoelectronic systems into precise locations of biological tissues provides powerful capabilities, especially in neuroscience such as optogenetics where light can activate/deactivate critical cellular signalling and neural systems. In such cases, engineered thermal management is essential, to avoid adverse effects of heating on normal biological processes. Here, an analytic model of heat conduction is developed for microscale, inorganic light-emitting diodes (μ-ILEDs) in a pulsed operation in biological tissues. The analytic solutions agree well with both three-dimensional finite-element analysis and experiments. A simple scaling law for the maximum temperature increase is presented in terms of material (e.g. thermal diffusivity), geometric (e.g. μ-ILED size) and loading parameters (e.g. pulsed peak power, duty cycle and frequency). These results provide useful design guidelines not only for injectable μ-ILED systems, but also for other similar classes of electronic and optoelectronic components. © 2013 The Author(s) Published by the Royal Society. All rights reserved.