We use wavelet and curvelet transforms to extract signals of cosmic strings from cosmic microwave background (CMB) temperature anisotropy maps, and to study the limits on the cosmic string tension which various ongoing CMB temperature anisotropy experiments will be able to achieve. We construct sky maps with size and angular resolution corresponding to various experiments. These maps contain the signals of a scaling solution of long string segments with a given string tension $G mu$, the contribution of the dominant Gaussian primordial cosmological fluctuations, and pixel by pixel white noise with an amplitude corresponding to the instrumental noise of the various experiments. In the case that we include white noise, we find that the curvelets are more powerful than wavelets. For maps with Planck specification, we obtain bounds on the string tension comparable to what was obtained by the Planck collaboration. Experiments with better angular resolution such as the South Pole Telescope third generation (SPT-3G) survey will be able to yield stronger limits. For maps with a specification of SPT-3G we find that string signals will be visible down to a string tension of $G mu = 1.4 times 10^{-7}$.
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