```typescript
export function runThermostat(start: number, low: number, high: number, power: number, drifts: number[]): { temp: number; heated: number; switches: number; coldest: number } {
  if (!Number.isInteger(start) || !Number.isInteger(low) || !Number.isInteger(high) || !Number.isInteger(power)) {
    throw new Error("Start, low, high and power must be integers.");
  }
  if (low >= high) {
    throw new Error("Low must be strictly below high.");
  }
  if (!Array.isArray(drifts)) {
    throw new Error("Drifts must be an array.");
  } else {
    for (const drift of drifts) {
      if (!Number.isInteger(drift)) {
        throw new Error("All drifts must be integers.");
      }
    }
  }

  let temp = start;
  let heated = 0;
  let switches = 0;
  let coldest = start;

  for (const drift of drifts) {
    if (temp < low) {
      heated++;
      switches += temp > coldest ? 1 : 0; // Count switch if current is colder
      coldest = Math.min(coldest, temp);
      temp += drift + power;
    } else if (temp >= high) {
      heated--;
      switches += temp < coldest ? 1 : 0; // Count switch if current is warmer
      coldest = Math.min(coldest, temp);
      temp += drift - power;
    } else {
      temp += drift;
    }
  }

  return { temp, heated, switches, coldest };
}
```