An electronic cigarette vaporiser that includes a heating element (35) and further includes or co-operates with an electronics module (58) that (i) detects characteristics of the resistance of the heating element (35) and (ii) uses an inference of temperature derived from that resistance as a control input. The temperature of the heating element (35) may be inferred from data stored in the electronics module (58) that has been empirically obtained for a specific heating element design. The electronics module (58) may controls the power delivered to the heating element (35) to ensure that it is no higher than approximately 130°C, plus an error tolerance. The module may use the resistance as an input directly, rather than calculating temperature. The module may also apply multiple techniques to control the temperature of the heating element and weigh the signal from each technique. Also disclosed is a re-filling and re-charging case (figure 6), into which the e-cigarette may be inserted. The vaporiser may be filled from a replaceable cartridge (3) via a piezo-electric pump (6), and may detect withdrawal from the case. The vaporiser may have a squircle cross-section (figure 2).
