We investigate the potential for aggregations of residential thermostatically controlled loads (TCLs), such as air conditioners, to arbitrage intraday wholesale electricity market prices via non-disruptive load control. We present two arbitrage approaches: 1) a benchmark that gives us an optimal policy but requires local computation or real-time communication and 2) an alternative based on a thermal energy storage model, which relies on less computation/communication infrastructure, but is suboptimal. We find that the alternative approach achieves around 60%-80% of the optimal wholesale energy cost savings. We use this approach to compute practical upper bounds for savings via arbitrage with air conditioners in California's intraday energy market. We investigate six sites over four years and find that the savings range from 2−37 per TCL per year, and depend upon outdoor temperature statistics and price volatility.