CMB lensing from current and upcoming wide-field CMB experiments such as
AdvACT, SPT-3G and Simons Observatory relies primarily on temperature, rather
than polarization. In this regime, foreground contamination to the temperature
maps produces significant lensing biases, which cannot be fully controlled by
multi-frequency component separation, masking or bias hardening. In this
letter, we use the different symmetries of the lensed CMB and foregrounds to
argue that a shear-only estimator should be approximately immune to
foregrounds. Using simulations, we build a new method to compute separately and
without noise the primary, secondary and trispectrum biases to CMB lensing. We
show that the shear estimator is indeed insensitive to foregrounds, even when
applied to a single-frequency temperature map contaminated with CIB, tSZ, kSZ
and radio point sources. This dramatic reduction in foreground biases allows us
to include higher temperature multipoles than with the standard quadratic
estimator, thus increasing the overall statistical power of lensing
measurements. In addition, the corresponding magnification-only estimator is
highly sensitive to foregrounds, and therefore provides a useful diagnostic for
potential residuals.